English Dictionary

Vitali-Carathéodory theorem

固有名詞

(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.

日本語の意味

ヴァイタリ・カラセドリーの定理とは、任意の実数値ルベーグ可積分関数が、上半連続関数で下から、また下半連続関数で上から任意の精度で近似できるという、数学解析における定理です。

During the lecture, the professor invoked the Vitali-Carathéodory theorem to construct an upper semicontinuous function that approximates a given Lebesgue integrable function from below.

講義中、教授は任意の実数値ルベーグ可積分関数が上半連続関数で下から、下半連続関数で上からそれぞれ任意に近似できるという定理（ヴィタリ＝カラテオドリの定理）を用いて、与えられた可積分関数を下から近似する上半連続関数を構成した。

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.