general lemma
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Ping-pong lemma — In mathematics, the ping pong lemma, or table tennis lemma, is any of several mathematical statements which ensure that several elements in a group acting on a set freely generate a free subgroup of that group.HistoryThe ping pong argument goes… … 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
Borel-Cantelli lemma — In probability theory, the Borel Cantelli lemma is a theorem about sequences of events. In a slightly more general form, it is also a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli.Let ( E n ) be a sequence… … Wikipedia
Schur's lemma — In mathematics, Schur s lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that that if M and N are two finite dimensional irreducible representations of a group G and… … Wikipedia
Nakayama lemma — In mathematics, more specifically modern algebra and commutative algebra, Nakayama s lemma also known as the Krull–Azumaya theorem[1] governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely… … Wikipedia
Pumping lemma for regular languages — In the theory of formal languages, the pumping lemma for regular languages describes an essential property of all regular languages. Informally, it says that all sufficiently long words in a regular language may be pumped that is, have a middle… … 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
Forking lemma — The forking lemma is any of a number of related lemmas in cryptography research. The lemma states that if an adversary (typically a probabilistic Turing machine), on inputs drawn from some distribution, produces an output that has some property… … Wikipedia
Tube lemma — In mathematics, particularly topology, the tube lemma is a useful tool in order to prove that the finite product of compact spaces is compact. It is in general, a concept of point set topology. Tube lemmaBefore giving the lemma, we note the… … 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
