All Questions
7 questions
13
votes
1
answer
616
views
reverse mathematics of the Lebesgue measurability of analytic sets
Can the fact that all analytic sets are Lebesgue measurable be proven in $Z_2$, or in some weak subsystem such as $\Pi^1_1\text{-CA}_0$? Conversely, can certain set existence axioms be derived from ...
- 2,130
11
votes
2
answers
483
views
The "strong" measure number
Beyond measure zero we have yet another measure-y notion of smallness: strong measure zero. A set $S\subseteq\mathbb{R}$ is strong measure zero if, for any $f:\mathbb{N}\rightarrow\mathbb{R}_{>0}$, ...
- 21.2k
13
votes
1
answer
751
views
Is there a class of mathematical structures with non-isomorphic natural representations as a standard Borel space?
Background. The field of Borel equivalence relation theory
provides a robust, unifying theory that organizes most of the
classification problems of classical mathematics into a hierarchy,
allowing us ...
- 236k
3
votes
0
answers
689
views
"Nicely" strong measure zero sets
This question is essentially an expanded version of the unanswered half of Two strengthenings of "strong measure zero".
A set $X$ of reals is strong measure zero if, for any $f: \omega\...
- 21.2k
18
votes
1
answer
772
views
Two strengthenings of "strong measure zero"
A set $X\subseteq\mathbb{R}$ is strong measure zero if, for every sequence $(\epsilon_i)_{i\in\mathbb{N}}$ of positive reals, there is a sequence $(I_i)_{i\in\mathbb{N}}$ of open intervals covering $X$...
- 21.2k
8
votes
0
answers
544
views
A Banach-Tarski game
This is partially inspired by the question https://math.stackexchange.com/questions/1383397/cutting-a-banach-tarski-cake, which I find intriguing if unclearly written.
A paradoxical family of subsets ...
- 21.2k
5
votes
3
answers
769
views
Cohen algebra (generalization)
Let Bor($X$) = class of all borel subsets of $X$. Cohen algebra is defined as Bor(X) modulo the ideal of meager sets.
The Cohen algebra has a combinatorial : it is the unique atomless complete ...
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