Category: Mathematical theorems

Ohsawa–Takegoshi L2 extension theorem
In several complex variables, the Ohsawa–Takegoshi L2 extension theorem is a fundamental result concerning the holomorphic extension of an -holomorphic function defined on a bounded Stein manifold (su
Buchdahl's theorem
In general relativity, Buchdahl's theorem, named after Hans Adolf Buchdahl, makes more precise the notion that there is a maximal sustainable density for ordinary gravitating matter. It gives an inequ
Mathematics of apportionment
Mathematics of apportionment describes mathematical principles and algorithms for fair allocation of identical items among parties with different entitlements. Such principles are used to apportion se
Pósa's theorem
Pósa's theorem, in graph theory, is a sufficient condition for the existence of a Hamiltonian cycle based on the degrees of the vertices in an undirected graph. It implies two other degree-based suffi
Maximum theorem
The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959
Minimax theorem
In the mathematical area of game theory, a minimax theorem is a theorem providing conditions that guarantee that the max–min inequality is also an equality. The first theorem in this sense is von Neum
Transport theorem
The transport theorem (or transport equation, rate of change transport theorem or basic kinematic equation) is a vector equation that relates the time derivative of a Euclidean vector as evaluated in
Trombi–Varadarajan theorem
In mathematics, the Trombi–Varadarajan theorem, introduced by Trombi and Varadarjan, gives an isomorphism between a certain space of spherical functions on a semisimple Lie group, and a certain space
Girsanov theorem
In probability theory, the Girsanov theorem tells how stochastic processes change under changes in measure. The theorem is especially important in the theory of financial mathematics as it tells how t
Classification theorem
In mathematics, a classification theorem answers the classification problem "What are the objects of a given type, up to some equivalence?". It gives a non-redundant enumeration: each object is equiva
Solovay–Kitaev theorem
In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2) then that set is guaranteed to fill SU(2
Universal chord theorem
In mathematical analysis, the universal chord theorem states that if a function f is continuous on [a,b] and satisfies , then for every natural number , there exists some such that .
Petersen–Morley theorem
In geometry, the Petersen–Morley theorem states that, ifa,b,care three general skew lines in space, ifa′,b′,c′ are the lines of shortest distancerespectively for the pairs (b,c), (c,a) and (a,b),and i
Toy theorem
In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation of the general theorem, or a framework for prov
Existence theorem
In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase "there exist(s)", or it might be a universal sta
Omega-categorical theory
In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism. Omega-categoricity is the special case κ = = ω of κ-categoricity, and om
Bauer maximum principle
Bauer's maximum principle is the following theorem in mathematical optimization: Any function that is convex and continuous, and defined on a set that is convex and compact, attains its maximum at som
Additive combinatorics
Additive combinatorics is an area of combinatorics in mathematics. One major area of study in additive combinatorics are inverse problems: given the size of the sumset A + B is small, what can we say
Kawasaki's theorem
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It stat
Sion's minimax theorem
In mathematics, and in particular game theory, Sion's minimax theorem is a generalization of John von Neumann's minimax theorem, named after Maurice Sion. It states: Let be a compact convex subset of
Fueter–Pólya theorem
The Fueter–Pólya theorem, first proved by Rudolf Fueter and George Pólya, states that the only quadratic polynomial pairing functions are the Cantor polynomials.
Chasles' theorem (kinematics)
In kinematics, Chasles' theorem, or Mozzi–Chasles' theorem, says that the most general rigid body displacement can be produced by a translation along a line (called its screw axis or Mozzi axis) follo
Bertrand's postulate
In number theory, Bertrand's postulate is a theorem stating that for any integer , there always exists at least one prime number with A less restrictive formulation is: for every , there is always at
Darmois–Skitovich theorem
The Darmois–Skitovich theorem is one of the most famous characterization theorems of mathematical statistics. It characterizes the normal distribution (the Gaussian distribution) by the independence o
Shell theorem
In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application t
Comparison theorem
In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often occur in fields such as calculus, differential eq
Jouanolou's trick
In algebraic geometry, Jouanolou's trick is a theorem that asserts, for an algebraic variety X, the existence of a surjection with affine fibers from an affine variety W to X. The variety W is therefo
Alexander–Hirschowitz theorem
The Alexander–Hirschowitz theorem shows that a specific collection of k double points in the P^r will impose independent types of conditions on homogenous polynomials and the hypersurface of d with ma
Budan's theorem
In mathematics, Budan's theorem is a theorem for bounding the number of real roots of a polynomial in an interval, and computing the parity of this number. It was published in 1807 by François Budan d
Approximate max-flow min-cut theorem
Approximate max-flow min-cut theorems are mathematical propositions in network flow theory. They deal with the relationship between maximum flow rate ("max-flow") and minimum cut ("min-cut") in a mult
Representation theorem
In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract or concrete) structure.
No free lunch theorem
In mathematical folklore, the "no free lunch" (NFL) theorem (sometimes pluralized) of David Wolpert and appears in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously derived no
Kostant's convexity theorem
In mathematics, Kostant's convexity theorem, introduced by Bertram Kostant, states that the projection of every coadjoint orbit of a connected compact Lie group into the dual of a Cartan subalgebra is
Grey box model
In mathematics, statistics, and computational modelling, a grey box model combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information
Stochastic portfolio theory
Stochastic portfolio theory (SPT) is a mathematical theory for analyzing stock market structure and portfolio behavior introduced by E. Robert Fernholz in 2002. It is descriptive as opposed to normati
Full-employment theorem
In computer science and mathematics, a full employment theorem is a term used, often humorously, to refer to a theorem which states that no algorithm can optimally perform a particular task done by so
Triangulation sensing
No description available.
Vincent's theorem
In mathematics, Vincent's theorem—named after —is a theorem that isolates the real roots of polynomials with rational coefficients. Even though Vincent's theorem is the basis of the fastest method for
Multiplication theorem
In mathematics, the multiplication theorem is a certain type of identity obeyed by many special functions related to the gamma function. For the explicit case of the gamma function, the identity is a
Zermelo's theorem (game theory)
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 chance does not affect the decision making proces