List of lemmas
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.
This list is incomplete; you can help by adding missing items. (August 2008) |
Algebra
- 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
- Abhyankar's lemma
- Fundamental lemma (Langlands program)
Category theory
Linear algebra
Group theory
- 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
- Gauss's lemma (polynomials)
- Schwartz–Zippel lemma
Ring theory and commutative algebra
- Artin–Rees lemma
- Hensel's lemma (commutative rings)
- Nakayama lemma
- Noether's normalization lemma
- Prime avoidance lemma
Universal algebra
Analysis
- 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
- Estimation lemma (contour integrals)
- Hartogs's lemma (several complex variables)
- Jordan's lemma
- Lemma on the Logarithmic derivative
- Schwarz lemma
Fourier analysis
Differential equations
- 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
Functional analysis
Mathematical series
Numerical analysis
Applied mathematics
- Danielson–Lanczos lemma (Fourier transforms)
- Farkas's lemma (linear programming)
- Feld–Tai lemma (electromagnetism)
- Little's lemma (queuing theory)
- Finsler's lemma
Control theory
Computational complexity theory
Cryptography
Formal languages
- Interchange lemma
- Newman's lemma (term rewriting)
- Ogden's lemma
- Pumping lemma sometimes called the Bar-Hillel lemma
Microeconomics
Combinatorics
- Cousin's lemma (integrals)
- Dickson's lemma
- Littlewood–Offord lemma
- Pólya–Burnside lemma
- Sperner's lemma
- Ky Fan lemma (combinatorial geometry)
Graph theory
- Berge's lemma
- Counting lemma
- Crossing lemma
- Expander mixing lemma
- Handshaking lemma
- Kelly's lemma
- Kőnig's lemma
- Szemerédi regularity lemma
Order theory
Dynamical systems
Geometry
Euclidean geometry
Hyperbolic geometry
Metric spaces
Riemannian geometry
- Gauss's lemma (Riemannian geometry)
Mathematical logic
- 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
- 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
- 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
Diophantine equations
Sieve theory
Probability theory
- Borel–Cantelli lemma
- Doob–Dynkin lemma
- Itô's lemma (stochastic calculus)
- Lovász local lemma
- Stein's lemma
- Wald's lemma
Statistics
Measure theory
- Factorization lemma
- Fatou's lemma
- Frostman's lemma (geometric measure theory)
- Malliavin's absolute continuity lemma