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Topics referred to by the same term
mathematics, there are several finiteness theorems. Ahlfors finiteness theorem Finiteness theorem for a proper morphism Compactness theorem, in mathematical logic
Finiteness_theorem
Mathematical theory
the Ahlfors finiteness theorem describes the quotient of the domain of discontinuity by a finitely generated Kleinian group. The theorem was proved by
Ahlfors_finiteness_theorem
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either
Classification of finite simple groups
Classification_of_finite_simple_groups
Rowell. The rank-finiteness theorem for G-crossed braided fusion categories is a theorem, also due to Jones et al. The rank-finiteness theorem for super-modular
Rank-finiteness
Topics referred to by the same term
ring is finitely generated Hilbert's finiteness theorem, in invariant theory, stating that the ring of invariants of a reductive group is finitely generated
Hilbert's_theorem
Theorems that help decompose a finite group based on prime factors of its order
mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter
Sylow_theorems
Theorem in algebra
In algebra, Zariski's finiteness theorem gives a positive answer to Hilbert's 14th problem for the polynomial ring in two variables, as a special case
Zariski's_finiteness_theorem
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under
Kruskal's_tree_theorem
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
On chains and antichains in partial orders
in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain of
Dilworth's_theorem
American mathematician (born 1943)
sums) with algebro-geometric methods. He introduced the Katz–Lang finiteness theorem. Gauss sums, Kloosterman sums, and monodromy groups. Annals of Mathematics
Nick_Katz
Consistent set of finite-dimensional distributions will define a stochastic process
extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees
Kolmogorov_extension_theorem
Theorems on the convergence of bounded monotonic sequences
In real analysis, the monotone convergence theorem is any of a number of related theorems proving, under certain conditions, the convergence of monotonic
Monotone_convergence_theorem
Theorem in Lie theory in mathematics
rigidity and finite generation of lattices the Kazhdan-Margulis theorem is an important ingredient in the proof of Wang's finiteness theorem. If G {\displaystyle
Kazhdan–Margulis_theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem, or the sampling theorem, is a theorem in the field of signal processing which serves as a fundamental bridge between
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Existence of group elements of prime order
In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number
Cauchy's theorem (group theory)
Cauchy's_theorem_(group_theory)
Branch of differential geometry
is diffeomorphic to a sphere. Cheeger's finiteness theorem. Given constants C, D and V, there are only finitely many (up to diffeomorphism) compact n-dimensional
Riemannian_geometry
Conditions for switching order of integration in calculus
the Fubini and Tonelli theorems are necessarily somewhat technical, as they have to use a hypothesis related to σ-finiteness. Most proofs involve building
Fubini's_theorem
On kernels of maps between abelianized fundamental groups of schemes and fields
Katz–Lang finiteness theorem, proved by Nick Katz and Serge Lang (1981), states that if X is a smooth, geometrically connected scheme of finite type over
Katz–Lang_finiteness_theorem
Commutative group where every element is the sum of elements from one finite subset
the fundamental theorem of finite abelian groups. The theorem, in both forms, in turn generalizes to the structure theorem for finitely generated modules
Finitely generated abelian group
Finitely_generated_abelian_group
Statement in abstract algebra
structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Equivalence of distributive lattices and set families
Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive
Birkhoff's representation theorem
Birkhoff's_representation_theorem
Hironaka theorem (algebraic geometry) Hodge index theorem (algebraic surfaces) Katz–Lang finiteness theorem (number theory) Lefschetz hyperplane theorem (algebraic
List_of_theorems
Theorem on the orders of subgroups
the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is a divisor
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Curves of genus > 1 over the rationals have only finitely many rational points
(1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae
Faltings'_theorem
Mathematical group based upon a finite number of elements
a theorem – the classification of finite simple groups. Inspection of the list of finite simple groups shows that groups of Lie type over a finite field
Finite_group
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean
Bolzano–Weierstrass_theorem
Theorem extending pre-measures to measures
In measure theory, Carathéodory's extension theorem (named after the mathematician Constantin Carathéodory) states that any pre-measure defined on a given
Carathéodory's extension theorem
Carathéodory's_extension_theorem
Statement in mathematical combinatorics
colour. An extension of this theorem applies to any finite number of colours, rather than just two. More precisely, the theorem states that for any given
Ramsey's_theorem
Polynomial ideals are finitely generated
mathematics, Hilbert's basis theorem asserts that every ideal of a polynomial ring over a field has a finite generating set (a finite basis in Hilbert's terminology)
Hilbert's_basis_theorem
Certain dynamical systems will eventually return to (or approximate) their initial state
In mathematics and physics, the Poincaré Recurrence Theorem states that if a system has a finite volume (or total probability measure) and preserves that
Poincaré_recurrence_theorem
Result in algebra
immediately yields a proof of the theorem as follows: let K be a finite field. Since the Herbrand quotient vanishes by finiteness, Br ( K ) = H 2 ( K al /
Wedderburn's_little_theorem
Subset of Euclidean space is compact if and only if it is closed and bounded
open cover of S {\displaystyle S} has a finite subcover S {\displaystyle S} is closed and bounded. The theorem is sometimes also called the Borel–Lebesgue
Heine–Borel_theorem
Concept in algebraic geometry
(2001) [1994], "Finiteness theorems", Encyclopedia of Mathematics, EMS Press Grauert, Hans; Remmert, Reinhold (2004). "The Finiteness Theorem". Theory of
Coherent_sheaf_cohomology
Finite collection of distinct objects
numerical concept of finiteness.) Ia-finite. For every partition of S {\displaystyle S} into two sets, at least one of the two sets is I-finite. (A set with this
Finite_set
Result about when a matrix can be diagonalized
on finite-dimensional vector spaces but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies
Spectral_theorem
Classification theorem in group theory
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s
Feit–Thompson_theorem
The group of K-rational points of an abelian variety is a finitely-generated abelian group
proof. Certainly the finiteness of this group is a necessary condition for E ( Q ) {\displaystyle E(\mathbb {Q} )} to be finitely generated; and it shows
Mordell–Weil_theorem
Relate the direct image and the pull-back of sheaves
1016/0022-4049(88)90102-8 Gabber, "Finiteness theorems for étale cohomology of excellent schemes" Grauert, Hans (1960), "Ein Theorem der analytischen Garbentheorie
Base_change_theorems
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Theorem in probability theory
particular, the theorem applies to doubling strategies and illustrates mathematically why such strategies cannot guarantee a profit with finite resources.
Optional_stopping_theorem
German mathematician (1862–1943)
demonstration in 1888 of his famous finiteness theorem. Twenty years earlier, Paul Gordan had demonstrated the theorem of the finiteness of generators for binary
David_Hilbert
Concerns the decomposition of representations of a finite group into irreducible pieces
Maschke's theorem, named after Heinrich Maschke, is a theorem in group representation theory that concerns the decomposition of representations of a finite group
Maschke's_theorem
Finnish mathematician (1907–1996)
in 1996. Ahlfors finiteness theorem Ahlfors function Ahlfors measure conjecture Beurling–Ahlfors transform Schwarz–Ahlfors–Pick theorem Measurable Riemann
Lars_Ahlfors
Branch of algebraic geometry
(1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae
Arithmetic_geometry
Certain polynomial equations in enough variables over a finite field have solutions
theory, the Chevalley–Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. It was
Chevalley–Warning_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Concept in measure theory
{\displaystyle \sigma } -finite. A different but related notion that should not be confused with σ {\displaystyle \sigma } -finiteness is s-finiteness. Let ( X , A
Σ-finite_measure
Expressing a measure as an integral of another
In mathematics, the Radon–Nikodym theorem, named after Johann Radon and Otto M. Nikodym, is a result in measure theory that expresses the relationship
Radon–Nikodym_theorem
Theorem in functional analysis
the main theorem uses essentially the same idea from the finite-dimensional argument. In the case that the operator is non-Hermitian, the theorem provides
Min-max_theorem
One of several theorems in different areas of mathematics
mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur
Schur's_theorem
Theorem
Superiore di Pisa - Classe di Scienze. 27 (4): 933–997. Parshin, A.N. (2001) [1994], "Finiteness theorems", Encyclopedia of Mathematics, EMS Press v t e
Andreotti–Grauert_theorem
In linear algebra, relation between 3 dimensions
The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity
Rank–nullity_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Counterintuitive result in probability
the monkey would almost surely type every possible finite text an infinite number of times. The theorem can be generalized to state that any infinite sequence
Infinite_monkey_theorem
Result in combinatorics and graph theory
mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and
Hall's_marriage_theorem
Characterizes the height of any finite partially ordered set
the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of a partition of the
Mirsky's_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Formal language that can be expressed using a regular expression
language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician
Regular_language
Method for representing and evaluating partial differential equations
surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a
Finite_volume_method
Commutative group (mathematics)
fundamental theorem of finitely generated abelian groups. The existence of algorithms for Smith normal form shows that the fundamental theorem of finitely generated
Abelian_group
In algebra, expression of an ideal as the intersection of ideals of a specific type
decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven
Primary_decomposition
Finitely many for a smooth algebraic curve of genus > 0 defined over a number field
In mathematics, Siegel's theorem on integral points states that a curve of genus greater than zero has only finitely many integral points over any given
Siegel's theorem on integral points
Siegel's_theorem_on_integral_points
Mathematical problem
Erdős–Ginzburg–Ziv theorem after its discoverers. It may also be deduced from the Cauchy–Davenport theorem. More general results than this theorem exist, such
Zero-sum_problem
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Representation of groups by permutations
is finite, Sym ( G ) {\displaystyle \operatorname {Sym} (G)} is finite too. The proof of Cayley's theorem in this case shows that if G is a finite group
Cayley's_theorem
Topological invariant in mathematics
finite by Grothendieck's finiteness theorem. This is an instance of the Euler characteristic of a chain complex, where the chain complex is a finite resolution
Euler_characteristic
Necessary and sufficient condition for a formal language to be regular
However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language
Myhill–Nerode_theorem
Mapping theorem in topology
of theorem, sometimes called Lefschetz-Hopf theorem counts fixed points with respect to their fixed-point index, provided that their number is finite. There
Lefschetz_fixed-point_theorem
Theorem in graph theory
In the mathematical discipline of graph theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number
Menger's_theorem
Statement in complex analysis
of complex analysis, the Hadamard factorization theorem asserts that every entire function with finite order can be represented as a product involving
Hadamard factorization theorem
Hadamard_factorization_theorem
Group without normal subgroups other than the trivial group and itself
for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple
Simple_group
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
In board games that cannot end in a draw, one of the two players has a winning strategy
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Theorem in measure theory
analysis, Lusin's theorem (or Luzin's theorem, named for Nikolai Luzin) or Lusin's criterion states that an almost-everywhere finite function is measurable
Lusin's_theorem
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Infinitely many prime numbers exist
proofs of the theorem. Euclid offered a proof in his work Elements (Book IX, Proposition 20), which is paraphrased here. Consider any finite list of prime
Euclid's_theorem
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Branch of number theory
significant number-theory problem formulated by Waring in 1770. As with the finiteness theorem, he used an existence proof that shows there must be solutions for
Algebraic_number_theory
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f {\displaystyle
Brouwer_fixed-point_theorem
Theorem in category theory
In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock
Beck's_monadicity_theorem
In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order
Trakhtenbrot's_theorem
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
Theorem in projective geometry
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in
Desargues's_theorem
Existence of a line through two points
The Sylvester–Gallai theorem in geometry states that every finite set of points in the Euclidean plane has a line that passes through exactly two of the
Sylvester–Gallai_theorem
Branch of logic
theory that fail for finite structures under finite model theory include the compactness theorem, Gödel's completeness theorem, and the method of ultraproducts
Finite_model_theory
German mathematician (1882–1935)
Endlichkeitssatz der Invarianten endlicher Gruppen" [The Finiteness Theorem for Invariants of Finite Groups] (PDF), Mathematische Annalen (in German), 77
Emmy_Noether
Mathematical theorem
the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector
Chevalley–Shephard–Todd theorem
Chevalley–Shephard–Todd_theorem
A prime p divides a^p–a for any integer a
In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In
Fermat's_little_theorem
Index of articles associated with the same name
In mathematics, a uniqueness theorem, also called a unicity theorem, is a theorem asserting the uniqueness of an object satisfying certain conditions,
Uniqueness_theorem
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Key results in general relativity on gravitational singularities
The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
About maxima and minima of functions
theorem states that any local extremum of a real function at which it is differentiable is a stationary point. It is also known as Fermat's theorem,
Interior_extremum_theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
Classification of semi-simple rings and algebras
algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras. The theorem states that a(n Artinian) semisimple
Wedderburn–Artin_theorem
Finiteness of sets of forbidden graph minors
under taking minors can be defined by a finite set of forbidden minors, in the same way that Wagner's theorem characterizes the planar graphs as being
Robertson–Seymour_theorem
Theorem of Fourier transforms of Borel measures
mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier-Stieltjes transform of a positive finite Borel measure on the real
Bochner's_theorem
Type of mathematical space
is the extreme value theorem. Another basic property of finite sets is that every cover of a finite set by subsets has a finite subcover: one may choose
Compact_space
Planar maps require at most four colors
In mathematics, the four color theorem, or the four-color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
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FINITENESS THEOREM
FINITENESS THEOREM
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FINITENESS THEOREM
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FINITENESS THEOREM
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