measure space

测度空间

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A measure space (X,A,mu) consists of a set X, a sigma-algebra A of its subsets, and a nonnegative extended-real function mu on A with mu(empty)=0 and countable additivity on disjoint measurable sets.

集合、其上的 σ 代数以及在该 σ 代数上非负、空集值为零且可列可加的测度，三者组成测度空间。

Example

([0,3],L,m)([0,3],\mathcal L,m) with restricted Lebesgue measure has total mass 33.

Usage and distinctions

A measurable space has only a set and sigma-algebra; a probability space additionally has total measure one.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. John K. Hunter — Measure Theory§1.6, Definition 1.9 and measure-space paragraph · Checked 2026-10-14

Translation sources

  1. 李东风（北京大学）— 金融时间序列分析备课笔记，附录EE.3 勒贝格测度，测度与测度空间段落 · Checked 2026-10-14
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