English Dictionary

complete measure

名詞

(mathematical analysis) A measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure.

日本語の意味

与えられた測度において、任意の測度ゼロの集合のすべての部分集合にも測度ゼロが割り当てられる性質を持つ測度。

To ensure convergence theorems hold, analysts often require that the underlying measure be a complete measure on the measurable space.

収束定理が成り立つようにするため、解析学者は基礎となる測度が可測空間上で任意の零集合のすべての部分集合に対して測度零を与える、すなわち完備測度であることを要求することが多い。

意味（1）

(mathematical analysis) A measure such that, for every set of measure zero belonging to its domain, all subsets of that set are also assigned measure zero by the given measure.

complete measures （ plural ）