Zbigniew Lipecki: How noncompact is the space of Lebesgue measurable sets?

Tuesday, May 30, 2023 17:00

Location: room A.4.1 C-19

Speaker:
Zbigniew Lipecki (IM PAN)

Title: How noncompact is the space of Lebesgue measurable sets?

Abstract: The space in question is the space \(\mathfrak M\) of Lebesgue measurable subsets of the unit interval equipped with the usual Fréchet—Nikodym (semi)metric.

We show that there exists a sequence of elements of \(\mathfrak M\) such that their mutual distances are > 1/2. It seems to be an open problem whether "1/2" can be replaced here by a bigger constant C. We show that C must be smaller than 9/14. Moreover, we present a version of the problem in terms of binary codes.