null set

零测集

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

Translation evidence: Literature usage

Meaning in context

A null set for a specified measure mu is a measurable set N with mu(N)=0.

相对于指定测度，测度值为零的可测集称为零测集；零测集未必是空集。

Example

Q∩[0,1]\mathbb Q\cap[0,1] is a Lebesgue null set although it is dense in [0,1][0,1].

Usage and distinctions

A subset of a null set need not be measurable unless the measure space is complete.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. John K. Hunter — Measure Theory§1.7, opening null-set 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，零测集段落 · Checked 2026-10-14
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