##  [Measure-Theoretic Boundary](/measure-theoretic-boundary) 

  ##  [Measure-Theoretic Boundary](https://mathlogic.quantumdictionary.io/measure-theoretic-boundary-0) 

  

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- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The set of points x in a measurable space such that every neighborhood of x has positive measure intersection with both the measurable set and its complement, considered up to null sets; equivalently the locus where the pointwise density of the set is neither 0 nor 1.