Mazur's lemma, the Glossary
In mathematics, Mazur's lemma is a result in the theory of normed vector spaces.[1]
Table of Contents
4 relations: Convex combination, Mathematics, Tonelli's theorem (functional analysis), Weak topology.
- Compactness theorems
- Lemmas in analysis
- Theorems involving convexity
Convex combination
In convex geometry and vector algebra, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.
See Mazur's lemma and Convex combination
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Mazur's lemma and Mathematics
Tonelli's theorem (functional analysis)
In mathematics, Tonelli's theorem in functional analysis is a fundamental result on the weak lower semicontinuity of nonlinear functionals on ''L''''p'' spaces. Mazur's lemma and Tonelli's theorem (functional analysis) are theorems in functional analysis.
See Mazur's lemma and Tonelli's theorem (functional analysis)
Weak topology
In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space.
See Mazur's lemma and Weak topology
See also
Compactness theorems
- Arzelà–Ascoli theorem
- Banach–Alaoglu theorem
- Blaschke selection theorem
- Bolzano–Weierstrass theorem
- Cantor's intersection theorem
- Eberlein–Šmulian theorem
- Fréchet–Kolmogorov theorem
- Fraňková–Helly selection theorem
- Gromov's compactness theorem (topology)
- Heine–Borel theorem
- Helly's selection theorem
- Kuratowski's intersection theorem
- Mahler's compactness theorem
- Mazur's lemma
- Michael selection theorem
- Montel's theorem
- Mumford's compactness theorem
- Prokhorov's theorem
- Sobolev inequality
Lemmas in analysis
- Aubin–Lions lemma
- Auerbach's lemma
- Borel's lemma
- Bramble–Hilbert lemma
- Céa's lemma
- Calderón–Zygmund lemma
- Closed and exact differential forms
- Cotlar–Stein lemma
- Ehrling's lemma
- Estimation lemma
- Fatou's lemma
- Fundamental lemma of the calculus of variations
- Grönwall's inequality
- Halanay inequality
- Itô's lemma
- Jordan's lemma
- Lebesgue's lemma
- Lions–Magenes lemma
- Malliavin's absolute continuity lemma
- Mazur's lemma
- Morse–Palais lemma
- Oka's lemma
- Poincaré lemma
- Pugh's closing lemma
- Riemann–Lebesgue lemma
- Riesz's lemma
- Rising sun lemma
- Sard's theorem
- Schwarz lemma
- Spijker's lemma
- Stechkin's lemma
- Stewart–Walker lemma
- Watson's lemma
- Weyl's lemma (Laplace equation)
- Wiener's lemma
Theorems involving convexity
- Convex conjugate
- Fenchel–Moreau theorem
- Hermite–Hadamard inequality
- Jensen's inequality
- Krein–Milman theorem
- Mazur's lemma
- Polar factorization theorem
- Riesz–Thorin theorem
- Ursescu theorem