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词汇 Counting measure
分类 英语词汇 英语翻译词典
释义

Counting measure

中文百科

计数测度

计数测度在数学上被定义为\mu \left ( E \right )=\left ( cardE \right ) 。 严格的说:计数测度是使得任一可测集的测度等于它含有的元素个数的那种测度。也就是说:对测度空间\left ( \Omega , F , \mu \right ),若对任意E\in F,都有: \mu \left ( E \right )=\left\{\begin{matrix}
card\left ( E \right ) &\left ( card\left ( E \right )< \aleph_{0} \right ) \\ 
 +\infty &\left ( card\left ( E \right )\geq  \aleph_{0} \right ) 
\end{matrix}\right.

则称\mu为测度空间\left ( \Omega , F , \mu \right )的计数测度。

英语百科

Counting measure 计数测度

In mathematics, the counting measure is an intuitive way to put a measure on any set: the "size" of a subset is taken to be the number of elements in the subset, if the subset has finitely many elements, and ∞ if the subset is infinite.

The counting measure can be defined on any measurable set, but is mostly used on countable sets.

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