English Dictionary

Vitali-Carathéodory theorem

name

(mathematical analysis) 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.

The Vitali-Carathéodory theorem is a fundamental result in measure theory.

意味（1）

(mathematical analysis) 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.