Let ##D## be a bounded subset of ##\mathbb{R}^m##; equip the set ##2^D## with the Hausdorff distance. We have obtained a semimetric space. Turn this space into a metric space by the corresponding factorization. Denote this factor space by ##F##. Let ##\overline F## stand for comleteion of ##F##.(adsbygoogle = window.adsbygoogle || []).push({});

Hypothesis. The standard Lebesgue ##\sigma-## algebra is an of first Baire category set in ##\overline F##.

(The inclusion ##\sigma \subset \overline F## is understood in sense of corresponding embeddings)

I tried to formalize an intuitive understanding (my understanding) that the set measurable subsets should be very small in the set of all subsets of ##\mathbb{R}^m##. Is that true what do you think?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Hypothesis on measurable sets

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**