extended lemma
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Fatou's lemma — In mathematics, Fatou s lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after the French… … Wikipedia
Massera's lemma — In stability theory and nonlinear control, Massera s lemma, named after José Luis Massera, deals with the construction of the Lyapunov function to prove the stability of a dynamical system.[1] The lemma appears in (Massera 1949, p. 716) as… … Wikipedia
Yoneda lemma — In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object . It is a vast generalisation of Cayley s theorem from group theory (a group being a particular kind of… … Wikipedia
Itō's lemma — In mathematics, Itō s lemma is used in Itō stochastic calculus to find the differential of a function of a particular type of stochastic process. It is the stochastic calculus counterpart of the chain rule in ordinary calculus and is best… … Wikipedia
Bramble-Hilbert lemma — In mathematics, particularly numerical analysis, the Bramble Hilbert lemma, named after James H. Bramble and Stephen R. Hilbert, bounds the error of an approximation of a function extstyle u by a polynomial of order at most extstyle m 1 in terms… … Wikipedia
Lindenbaum's lemma — In mathematical logic, Lindenbaum s lemma states that any consistent theory of predicate logic can be extended to a complete consistent theory. It is used in the proof of Gödel s completeness theorem, among other places. The lemma is a special… … Wikipedia
Handshaking lemma — In this graph, an even number of vertices (the four vertices numbered 2, 4, 5, and 6) have odd degrees. The sum of the degrees of the vertices is 2 + 3 + 2 + 3 + 3 + 1 = 14, twice the… … Wikipedia
Piling-up lemma — In cryptanalysis, the piling up lemma is a principle used in linear cryptanalysis to construct linear approximations to the action of block ciphers. It was introduced by Mitsuru Matsui (1993) as an analytical tool for linear… … Wikipedia
Hensel's lemma — In mathematics, Hensel s lemma, named after Kurt Hensel, is a generic name for analogues for complete commutative rings (including p adic fields in particular) of the Newton method for solving equations. Since p adic analysis is in some ways… … Wikipedia
Itō calculus — Itō calculus, named after Kiyoshi Itō, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations.The central… … Wikipedia
Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most … Wikipedia
