Complete measure space | Wikipedia audio article
Channel: wikipedia tts
Date: 29/03/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Complete_measure


00:00:50 1 Motivation
00:03:04 2 Construction of a complete measure
00:05:16 3 Examples
00:06:21 4 Properties



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Speaking Rate: 0.8206557106450457
Voice name: en-GB-Wavenet-B


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, a complete measure (or, more precisely, a complete measure space) is a measure space in which every subset of every null set is measurable (having measure zero). More formally, a measure space (X, Σ, μ) is complete if and only if

  
    
      
        S
        ⊆
        N
        ∈
        Σ
        
          
             and 
          
        
        μ
        (
        N
        )
        =
        0
         
        ⇒
         
        S
        ∈
        Σ
        .
      
    
    {\displaystyle S\subseteq N\in \Sigma {\mbox{ and }}\mu (N)=0\ \Rightarrow \ S\in \Sigma .}