Simple question about Lebesgue and Borel sigma algebra

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Homework Help Overview

The discussion revolves around the properties of Lebesgue measure and Borel sets, specifically addressing whether a Borel set of null measure can contain a set of null Lebesgue measure.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between null sets in Lebesgue measure and Borel sets, questioning the containment of one within the other.

Discussion Status

Some participants have provided insights regarding the nature of Borel sets and their relationship to Lebesgue measure, while others have reiterated the original question, indicating a mix of understanding and clarification efforts.

Contextual Notes

There appears to be some confusion regarding the direction of containment between the null sets and Borel sets, as well as the implications of Lebesgue measure's regularity.

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If N is of null Lebesgue measure. Can we find a Borel set B of null measure such that N is entirely contained in B?
 
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The empty set!
 
it's the other way around. we want B borel such that N is contained in B
 
bump!
 
quasar987 said:
it's the other way around. we want B borel such that N is contained in B
Oops!

This is also true. It follows from the fact that the Lebesgue measure is regular.
 

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