Vitali-Carathéodory theorem

Vitali-Carathéodory theorem
A theorem which states that any real-valued Lebesgue integrable function can be approached arbitrarily closely from below by an upper semicontinuous function and also from above by a lower semicontinuous function.

Wikipedia foundation.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • List of theorems — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… …   Wikipedia

  • Liste de théorèmes — par ordre alphabétique. Pour l établissement de l ordre alphabétique, il a été convenu ce qui suit : Si le nom du théorème comprend des noms de mathématiciens ou de physiciens, on se base sur le premier nom propre cité. Si le nom du théorème …   Wikipédia en Français

  • Lebesgue measure — In mathematics, the Lebesgue measure, named after Henri Lebesgue, is the standard way of assigning a length, area or volume to subsets of Euclidean space. It is used throughout real analysis, in particular to define Lebesgue integration. Sets… …   Wikipedia

  • Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”