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...branch of mathematics, the '''condensation lemma''' is a result about sets in the ...sub>&alpha;</sub>, that is, <math>(X,\in)\prec (L_\alpha,\in)</math>, then in fact there is some ordinal <math>\beta\leq\alpha</math> such that <math>X=L ...

In the theory of [[formal language]]s, the '''interchange lemma''' states a necessary con ...er, <math>m/2<|x_i|\leq m</math>, and the words <math>w_ix_jy_i</math> are in <math>L</math> for every <math>i</math> and <math>j</math>. ...

...spect to [[inclusion (set theory)|inclusion]]. Over [[Zermelo–Fraenkel set theory]], the Teichmüller–Tukey lemma is equivalent to the [[axiom of choice]], an #For each <math>A\in \mathcal{F}</math>, every [[finite set|finite]] [[subset]] of <math>A</math> belongs to <math>\mathcal{F}</math>. ...

...g and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. * [[Digital Morse theory]] ...

In [[mathematics]], '''Cartan's lemma''' refers to a number of results named a * In [[exterior algebra]]:<ref>*{{cite book | last = Sternberg | first = S. | ye ...

...lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the ...ty <math>d(U,V)</math>, is ''close'' ''to being'' a random bipartite graph in which every edge appears with probability <math>d(U,V)</math>, with some <m ...

{{Short description|Theorem in functional analysis}} ...ics, '''Auerbach's lemma''', named after [[Herman Auerbach]], is a theorem in [[functional analysis]] which asserts that a certain property of [[Euclidea ...

...emma describing the behaviour of pseudo-orbits near a hyperbolic invariant set}} ...mly close to some true trajectory (with slightly altered initial position)—in other words, a pseudo-trajectory is "shadowed" by a true one.<ref>{{cite jo ...

...sis of a [[function space]]. The result was originally proved by Stechkin in the case <math>q = 2</math>. ...math>N</math> largest terms of the sequence <math>(a_{i})_{i \in I}</math> in [[absolute value]]. Then ...

The '''Mackey–Arens theorem''' is an important theorem in [[functional analysis]] that characterizes those [[locally convex]] [[Topol ...system|duality theory]]; a theory that is "the central part of the modern theory of topological vector spaces."{{sfn | Schaefer|Wolff| 1999 | p=122}} ...

...m the commutations required by the [[Poincaré–Birkhoff–Witt theorem]] used in the construction of a [[universal enveloping algebra]]. As such, this gener ...ng process]] was described first, in 1934, by [[Philip Hall]] and explored in 1937 by [[Wilhelm Magnus]].<ref> ...

In [[theoretical computer science]], the term '''isolation lemma''' (or '''iso ...nt–Vazirani theorem]] and [[Toda's theorem]] in [[computational complexity theory]]. ...

The '''Steinitz exchange lemma''' is a basic theorem in [[linear algebra]] used, for example, to show that any two [[Basis (linear ...ac Lane|year=1936|title=Some interpretations of abstract linear dependence in terms of projective geometry|journal=American Journal of Mathematics|volume ...

...king lemma''' is any of a number of related [[lemma (mathematics)|lemmas]] in [[cryptography]] research. The lemma states that if an adversary (typicall ...ry Neven, "[http://portal.acm.org/citation.cfm?id=1180453 Multi-Signatures in the Plain Public-Key Model and a General Forking Lemma]", Proceedings of th ...

{{Short description|Type of graph in mathematics}} In [[graph theory]], a branch of [[mathematics]], a '''half graph''' is a special type of [[b ...

...in ergodic theory, for example in [[Ornstein isomorphism theorem|Ornstein theory]] and has many generalizations. ...is which are traditionally called lemmas despite the fact that their roles in their respective fields are fundamental. ...

...hochman/courses/ergodic-theory-2012/notes.final.pdf|title=Notes on ergodic theory|last=Hochman|first=Michael|date=2013-01-27|website=|page=20|archive-url=|ar ...arles.walkden/magic/default.htm|title=MAGIC: 10 lectures course on ergodic theory – Lecture 5|last=Walkden|first=Charles|date=|website=|archive-url=|archive- ...

...of of the [[Hardy–Littlewood maximal theorem]]. The lemma was a precursor in one dimension of the [[Calderón–Zygmund lemma]].<ref>{{harvnb|Stein|1998}}< ...(''x'',''b''] with ''g''(''y'') > ''g''(''x''). (Note that ''b'' cannot be in ''S'', though ''a'' may be.) Define ''E'' = ''S'' ∩ (''a'',''b''). ...

{{Short description|Method in combinatorics}} ...], and [[Ramsey theory]]; they include some of the most classical problems in the associated fields. ...

...lemma in [[convex geometry]] and [[algebraic geometry]]. It can be stated in several ways. ...a, Steinitz' lemma and invariant theory | journal=Journal of Combinatorial Theory, Series A | volume=43 | issue=1 | pages=91–97 | doi=10.1016/0097-3165(86)90 ...