English Dictionary

Lebesgue integral

IPA（発音記号）

/ləˈbɛːɡ ˈɪntəɡɹəl/

名詞

可算名詞 定冠詞 単数形 単数形のみ

(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).

日本語の意味

ルベーグ積分：リーマン積分よりも広範な場合に適用可能な積分法であり、積分領域を単なる区間ではなく、測度可能な任意の集合に分割できるため、関数の値域が十分に限定される場合に積分が可能となる。

To compute the expectation of the random variable rigorously, we used the Lebesgue integral over the probability space.

確率空間上で確率変数の期待値を厳密に計算するために、ルベーグ積分を用いました。

意味（1）

(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).

The Lebesgue integral is learned in a first-year real-analysis course.

Lebesgue integrals （ plural ）