List of lemmas
From Wikipedia - Reading time: 4 min
This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list of axioms, list of theorems and list of conjectures.
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Algebra
[edit]- Abhyankar's lemma
- Aubin–Lions lemma
- Bergman's diamond lemma
- Fitting lemma
- Injective test lemma
- Hua's lemma (exponential sums)
- Krull's separation lemma
- Schanuel's lemma (projective modules)
- Schwartz–Zippel lemma
- Shapiro's lemma
- Stewart–Walker lemma (tensors)
- Whitehead's lemma (Lie algebras)
- Zariski's lemma
Algebraic geometry
[edit]Category theory
[edit]
Linear algebra
[edit]Group theory
[edit]- Burnside's lemma also known as the Cauchy–Frobenius lemma
- Frattini's lemma (finite groups)
- Goursat's lemma
- Mautner's lemma (representation theory)
- Ping-pong lemma (geometric group theory)
- Schreier's subgroup lemma
- Schur's lemma (representation theory)
- Zassenhaus lemma
Polynomials
[edit]Ring theory and commutative algebra
[edit]- Artin–Rees lemma
- Hensel's lemma (commutative rings)
- Nakayama lemma
- Noether's normalization lemma
- Prime avoidance lemma
Universal algebra
[edit]Analysis
[edit]- Fekete's lemma
- Fundamental lemma of calculus of variations
- Hopf lemma
- Sard's lemma (singularity theory)
- Stechkin's lemma (functional and numerical analysis)
- Vitali covering lemma (real analysis)
- Watson's lemma
Complex analysis
[edit]- Estimation lemma (contour integrals)
- Hartogs's lemma (several complex variables)
- Jordan's lemma
- Lemma on the Logarithmic derivative
- Schwarz lemma
Fourier analysis
[edit]Differential equations
[edit]- Borel's lemma (partial differential equations)
- Grönwall's lemma
- Lax–Milgram lemma
- Pugh's closing lemma
- Weyl's lemma (Laplace equation) (partial differential equations)
Differential forms
[edit]Functional analysis
[edit]Mathematical series
[edit]Numerical analysis
[edit]Applied mathematics
[edit]
- Danielson–Lanczos lemma (Fourier transforms)
- Farkas's lemma (linear programming)
- Feld–Tai lemma (electromagnetism)
- Little's lemma (queuing theory)
- Finsler's lemma
Control theory
[edit]Computational complexity theory
[edit]Cryptography
[edit]Formal languages
[edit]- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
[edit]Combinatorics
[edit]- Cousin's lemma (integrals)
- Dickson's lemma
- Littlewood–Offord lemma
- Pólya–Burnside lemma
- Sperner's lemma
- Ky Fan lemma (combinatorial geometry)
Graph theory
[edit]- Berge's lemma
- Counting lemma
- Crossing lemma
- Expander mixing lemma
- Handshaking lemma
- Kelly's lemma
- Kőnig's lemma
- Szemerédi regularity lemma
Order theory
[edit]Dynamical systems
[edit]Geometry
[edit]Euclidean geometry
[edit]Hyperbolic geometry
[edit]Metric spaces
[edit]Riemannian geometry
[edit]Mathematical logic
[edit]- Craig interpolation lemma
- Diagonal lemma
- Lindenbaum's lemma
- Mostowski collapse lemma
- Teichmüller–Tukey lemma also known as Tukey's lemma
- Zorn's lemma; equivalent to the axiom of choice
Set theory
[edit]- Covering lemma
- Delta lemma
- Dynkin lemma
- Fodor's lemma
- Fixed-point lemma for normal functions (axiomatic set theory)
- Moschovakis coding lemma
- Rasiowa–Sikorski lemma
Number theory
[edit]- Bézout's lemma
- Dwork's lemma
- Euclid's lemma
- Gauss's lemma
- Hensel's lemma
- Zolotarev's lemma
- Siegel's lemma (Diophantine approximation)
Analytic number theory
[edit]Diophantine equations
[edit]Sieve theory
[edit]Probability theory
[edit]- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma
Statistics
[edit]Measure theory
[edit]- Factorization lemma
- Fatou's lemma
- Frostman's lemma (geometric measure theory)
- Malliavin's absolute continuity lemma
Topology
[edit]Differential topology
[edit]Fixed-point theory
[edit]
Geometric topology
[edit]Topological groups and semigroups
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