Category

Theorems in measure theory

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isoperimetric inequality

geometric inequality which sets a lower bound on the surface area of a set given its volume

Borel–Cantelli lemma

mathematical sentence

Fubini's theorem

Radon–Nikodym theorem

fundamental result in measure theory that expresses the relationship between two measures defined on the same measurable space

dominated convergence theorem

theorem that, for a sequence of functions bounded in absolute value by an integrable function, then almost everywhere pointwise convergence implies L¹ convergence

inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions

monotone convergence theorem

theorem of calculus

Lusin's theorem

ham sandwich theorem

theorem that any three objects in space can be simultaneously bisected by a plane

Egorov's theorem

theorem that the set of the critical values of a smooth function has measure zero

Rademacher's theorem

Lebesgue differentiation theorem

in real analysis, the theorem that, for almost every point, the value of an integrable function is the limiting average taken around the point

Hahn decomposition theorem

Brunn–Minkowski theorem

theorem in geometry

Carathéodory's extension theorem

theorem extending pre-measures to measures

Lebesgue's density theorem

theorem that, the density of a Lebesgue measurable set in Euclidean space is exists and is 0 or 1 almost everywhere

Lebesgue's decomposition theorem

vitali convergence theorem

mathematical theorem

Prokhorov's theorem

relates tightness of measures to relative compactness in the space of probability measures

Cramér–Wold theorem

theorem in measure theory

Alexandrov's theorem

theorem about convex functions

Steinhaus theorem

mathematical theorem in real analysis

Bochner's theorem

theorem of Fourier transforms of Borel measures

Fubini's theorem on differentiation

Krylov–Bogolyubov theorem

F. and M. Riesz theorem

Scheffé’s lemma

result in measure theory