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词汇 Jordan measure
分类 英语词汇 英语翻译词典
释义

Jordan measure

中文百科

若尔当测度

A simple set is, by definition, a union of (possibly overlapping) rectangles.
The simple set from above decomposed as a union of non-overlapping rectangles.
A set (represented in the picture by the region inside the blue curve) is Jordan measurable if and only if it can be well-approximated both from the inside and outside by simple sets (their boundaries are shown in dark green and dark pink respectively).

若尔当测度（Jordan measure）是面积测度方式，数学家卡米尔·若尔当所提出。设E是R^{n}中的一个有界集，而f是在E上取值为1的函数，如果f在E上可积，则称E为Jordan可测的（可求体积的）。并且记\int_{E}^{ }1dx=\mu \left(E \right)，称为E的Jordan测度，也就是E的体积。

英语百科

Jordan measure 若尔当测度

A simple set is, by definition, a union of (possibly overlapping) rectangles.
The simple set from above decomposed as a union of non-overlapping rectangles.
A set (represented in the picture by the region inside the blue curve) is Jordan measurable if and only if it can be well-approximated both from the inside and outside by simple sets (their boundaries are shown in dark green and dark pink respectively).

In mathematics, the Peano–Jordan measure (also known as the Jordan content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped.

It turns out that for a set to have Jordan measure it should be well-behaved in a certain restrictive sense. For this reason, it is now more common to work with the Lebesgue measure, which is an extension of the Jordan measure to a larger class of sets. Historically speaking, the Jordan measure came first, towards the end of the nineteenth century.
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