Statements
A theorem, a lemma, a proposition, a corollary, a fact or an axiom.
- Concepts 5206
- Definitions 5027
- Statements 3081
- Conjectures 75
- Problems 147
- Examples 431
- Counterexamples 71
- Objects 132
- Proofs 11
- Computations 1
- Topics 1
Ideas 2101–2250 of 3081.
| Name | Kind | Subject |
|---|---|---|
| Dvoretzky–Kiefer–Wolfowitz inequality | Theorem | Statistics |
| Convergence of approximations for second-kind equations | Theorem | Integral equations |
| Layer cake representation | Theorem | Measure and integration |
| Jacobson radical of an Artinian ring is nilpotent | Theorem | Associative rings and algebras |
| Lions–Stampacchia theorem | Theorem | Calculus of variations and optimal control; optimization |
| Green–Tao theorem | Theorem | Number theory |
| Dvoretzky–Rogers theorem | Theorem | Functional analysis |
| Double centralizer theorem | Theorem | Associative rings and algebras |
| Berry–Esseen theorem | Theorem | Probability theory and stochastic processes |
| Hodge decomposition | Theorem | Algebraic geometry |
| Interpolation error formula | Theorem | Approximations and expansions |
| Annulus theorem | Theorem | Manifolds and cell complexes |
| Christoffel–Darboux formula | Theorem | Harmonic analysis on Euclidean spaces |
| Gromov's systolic inequality | Theorem | Differential geometry |
| Urysohn metrization theorem | Theorem | General topology |
| Continuity of measure from below and above | Proposition | Measure and integration |
| Riemann localization principle | Theorem | Harmonic analysis on Euclidean spaces |
| Capelli's theorem | Theorem | Field theory and polynomials |
| Zariski's main theorem | Theorem | Commutative algebra |
| Bernstein's theorem on inverse approximation | Theorem | Approximations and expansions |
| Structure theorem for Artinian rings | Theorem | Commutative algebra |
| Gordan's lemma | Lemma | Convex and discrete geometry |
| Poincaré–Birkhoff–Witt theorem | Theorem | Nonassociative rings and algebras |
| Hardy–Littlewood–Sobolev inequality | Theorem | Harmonic analysis on Euclidean spaces |
| Biconjugate gradient method | Theorem | Numerical analysis |
| Docquier–Grauert theorem | Theorem | Several complex variables and analytic spaces |
| Gabrielov's theorem of the complement | Theorem | Several complex variables and analytic spaces |
| Differentiation and multiplication under the Fourier transform | Proposition | Harmonic analysis on Euclidean spaces |
| Variational principle for topological entropy | Theorem | Dynamical systems and ergodic theory |
| Lie product formula | Theorem | Linear and multilinear algebra; matrix theory |
| Shannon–McMillan–Breiman theorem | Theorem | Dynamical systems and ergodic theory |
| Kolmogorov criterion for best approximation | Theorem | Approximations and expansions |
| Thom's cobordism theorem | Theorem | Manifolds and cell complexes |
| Abel–Plana formula | Theorem | Numerical analysis |
| Radon inversion formula | Theorem | Integral transforms, operational calculus |
| Kronecker's lemma | Lemma | Sequences, series, summability |
| Hilbert–Serre theorem | Theorem | Commutative algebra |
| Plancherel theorem | Theorem | Harmonic analysis on Euclidean spaces |
| Sperner's lemma | Lemma | Combinatorics |
| Cochran's theorem | Theorem | Statistics |
| Freedman's classification of simply connected 4-manifolds | Theorem | Manifolds and cell complexes |
| Schauder estimates | Theorem | Partial differential equations |
| Universal approximation theorem | Theorem | Approximations and expansions |
| Path lifting property | Theorem | Manifolds and cell complexes |
| Crandall–Lions uniqueness theorem | Theorem | Calculus of variations and optimal control; optimization |
| Jenkins–Traub algorithm | Theorem | Numerical analysis |
| Kronecker's approximation theorem | Theorem | Number theory |
| Hausdorff–Young inequality | Theorem | Harmonic analysis on Euclidean spaces |
| Stewart's theorem | Theorem | Geometry |
| Iterated Laplace transform equals Stieltjes transform | Proposition | Integral transforms, operational calculus |
| Associativity of convolution | Proposition | Integral transforms, operational calculus |
| Erdős–Ginzburg–Ziv theorem | Theorem | Number theory |
| Tait conjectures | Theorem | Manifolds and cell complexes |
| Janson inequality | Theorem | Combinatorics |
| Matrix rings over simple rings are simple | Proposition | Associative rings and algebras |
| Dispersive estimate for the Schrödinger equation | Theorem | Partial differential equations |
| Descartes' theorem | Theorem | Geometry |
| Quasi-compactness of the spectrum | Proposition | Algebraic geometry |
| Jump relations for layer potentials | Theorem | Potential theory |
| Pettis lemma | Lemma | Topological groups, Lie groups |
| Hilbert projection theorem | Theorem | Functional analysis |
| Birkhoff's ergodic theorem | Theorem | Dynamical systems and ergodic theory |
| Grothendieck duality | Theorem | Algebraic geometry |
| Sierpiński's theorem on non-atomic measures | Theorem | Measure and integration |
| Projection-slice theorem | Theorem | Integral transforms, operational calculus |
| Kac's lemma | Lemma | Dynamical systems and ergodic theory |
| Runge–Kutta method for stochastic differential equations | Theorem | Numerical analysis |
| Mori–Nagata theorem | Theorem | Commutative algebra |
| Rodrigues' formula | Theorem | Special functions |
| Prékopa–Leindler inequality | Theorem | Real functions |
| Schauder's theorem on adjoints of compact operators | Theorem | Operator theory |
| Kojima–Schur theorem | Theorem | Sequences, series, summability |
| Riesz's subsequence theorem | Theorem | Measure and integration |
| Symmetry of the Green function | Theorem | Potential theory |
| Carathéodory's criterion | Theorem | Measure and integration |
| Lomonosov's invariant subspace theorem | Theorem | Operator theory |
| Morita equivalence of a ring with its matrix rings | Theorem | Associative rings and algebras |
| Schauder fixed-point theorem for integral equations | Corollary | Integral equations |
| Spectral theory of compact operators | Theorem | Operator theory |
| Newman's theorem on rational approximation of the absolute value | Theorem | Approximations and expansions |
| Jacobi triple product | Theorem | Number theory |
| Correspondence theorem for congruences | Theorem | General algebraic systems |
| Fáry's theorem | Theorem | Combinatorics |
| Catalan's conjecture | Theorem | Number theory |
| Eckart–Young theorem | Theorem | Linear and multilinear algebra; matrix theory |
| Four lemma | Lemma | Category theory; homological algebra |
| Legendre–Hadamard condition | Theorem | Calculus of variations and optimal control; optimization |
| Little's law | Theorem | Probability theory and stochastic processes |
| Fundamental lemma of the calculus of variations | Lemma | Calculus of variations and optimal control; optimization |
| Skorokhod's representation theorem | Theorem | Probability theory and stochastic processes |
| Hölder's inequality | Theorem | Real functions |
| Ultraparallel theorem | Theorem | Geometry |
| Â-genus as the index of the Dirac operator | Theorem | Global analysis, analysis on manifolds |
| Lê–Ramanujam theorem | Theorem | Several complex variables and analytic spaces |
| Cheeger's inequality for the first eigenvalue | Theorem | Global analysis, analysis on manifolds |
| Poincaré inequality | Theorem | Functional analysis |
| Linearized stability theorem for maps | Theorem | Difference and functional equations |
| Hewitt–Savage zero–one law | Theorem | Probability theory and stochastic processes |
| Lindström–Gessel–Viennot lemma | Lemma | Combinatorics |
| Open embedding theorem for Hilbert manifolds | Theorem | Global analysis, analysis on manifolds |
| Shift property of the Z-transform | Proposition | Integral transforms, operational calculus |
| Fischer decomposition | Theorem | Potential theory |
| Young's convolution inequality | Theorem | Integral transforms, operational calculus |
| Jensen's inequality for integrals | Theorem | Real functions |
| Favard's theorem on trigonometric approximation | Theorem | Approximations and expansions |
| Kontsevich quantization formula | Theorem | Differential geometry |
| Existence of limits from products and equalizers | Theorem | Category theory; homological algebra |
| Dimension of the solution space of a linear recurrence | Theorem | Difference and functional equations |
| Hammersley–Clifford theorem | Theorem | Statistics |
| Borel–Weil–Bott theorem | Theorem | Topological groups, Lie groups |
| Local parametrization theorem | Theorem | Several complex variables and analytic spaces |
| Calderón–Zygmund lemma | Lemma | Harmonic analysis on Euclidean spaces |
| Jacobi eigenvalue algorithm | Theorem | Numerical analysis |
| Bramble–Hilbert lemma | Lemma | Numerical analysis |
| Goldstine theorem | Theorem | Functional analysis |
| Brauer–Fowler theorem | Theorem | Group theory and generalizations |
| Strang splitting | Theorem | Numerical analysis |
| Reflection principle | Theorem | Probability theory and stochastic processes |
| Poincaré–Birkhoff theorem | Theorem | Dynamical systems and ergodic theory |
| de Rham theorem | Theorem | Global analysis, analysis on manifolds |
| Miquel's theorem | Theorem | Geometry |
| Fractional Helly theorem | Theorem | Convex and discrete geometry |
| Pick's theorem | Theorem | Convex and discrete geometry |
| Pfaff and Euler transformations | Theorem | Special functions |
| Nagata–Smirnov metrization theorem | Theorem | General topology |
| Existence and uniqueness of Haar measure | Theorem | Measure and integration |
| Isoperimetric inequality | Theorem | Convex and discrete geometry |
| Cartan–Brauer–Hua theorem | Theorem | Associative rings and algebras |
| Van Vleck's theorem | Theorem | Sequences, series, summability |
| Sphere eversion | Theorem | Manifolds and cell complexes |
| Contraction mapping principle for integral equations | Theorem | Integral equations |
| Bergman's gap theorem | Theorem | Associative rings and algebras |
| Density of trigonometric polynomials in continuous functions | Theorem | Harmonic analysis on Euclidean spaces |
| Jordan decomposition of a function of bounded variation | Theorem | Real functions |
| Freiman's theorem | Theorem | Number theory |
| Differentiable dependence on parameters | Theorem | Ordinary differential equations |
| Jacobi–Anger expansion | Proposition | Special functions |
| Lie–Trotter product formula | Theorem | Operator theory |
| Abel transform as the projection of a radial function | Proposition | Integral transforms, operational calculus |
| Ill-posedness of first-kind equations | Theorem | Integral equations |
| Routh–Hurwitz stability criterion | Theorem | Real functions |
| Pasch's axiom | Fact | Geometry |
| Alexander duality | Theorem | Algebraic topology |
| Kuratowski embedding | Theorem | General topology |
| Douglas–Radó solution of Plateau's problem | Theorem | Calculus of variations and optimal control; optimization |
| Riemann–Hilbert correspondence | Theorem | Several complex variables and analytic spaces |
| Hermite–Minkowski theorem | Theorem | Number theory |
| Koebe's theorem on the mean value property | Theorem | Potential theory |
| Nonexistence of a projective plane of order 10 | Theorem | Geometry |
| Wiener–Ikehara theorem | Theorem | Number theory |