Zbigniew Lipecki: How noncompact is the space of Lebesgue measurable sets?
24/05/23 11:41
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.
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.