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16 votes
4 answers
2k views

Is there a maximum to the amount of disjoint non-measurable subsets of the unit interval with full outer measure?

This question arose a few years back when I was an assistant teacher on a course of basic (Lebesgue) measure theory, but I didn't find an answer or anyone able to solve the problem. The setting of the ...
Rami Luisto's user avatar
7 votes
2 answers
665 views

Non-separable metric probability space

Let us say a metric probability space $(X,\rho,\mu)$ has property (*) if: the support of $\mu$ is contained in a separable subspace of $X$. Questions: 1. Is there a standard name for this property? ...
Aryeh Kontorovich's user avatar
2 votes
0 answers
240 views

3 questions around the Stone space of the free $\sigma$-algebra on $\omega_1$ free generators

During my studies, I came across several different Stone spaces, e.g.: (i) The Cantor cube $X=\{0,1\}^{\omega_1}$, which is the Stone space of the free Boolean algebra on $\omega_1$ free generators; ...
LJGC's user avatar
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