User Alexander Pruss

20 votes

0 answers

392 views

Hahn-Banach and the "Axiom of Probabilistic Choice"

asked Sep 14, 2017 at 14:57

19 votes

2 answers

983 views

How many subsets of $[0,1)$ are there modulo null sets?

asked Mar 19, 2015 at 20:34

14 votes

1 answer

332 views

Comparing sizes of sets of integers

asked Sep 2, 2020 at 16:09

10 votes

0 answers

734 views

Full conditional probabilities and versions of AC?

asked Nov 21, 2013 at 14:47

10 votes

0 answers

252 views

Strength of claims about extensions of partial preorders and orders to linear ones

asked Dec 5, 2013 at 18:06

9 votes

2 answers

447 views

Hyperreal finitely-additive measure on [0,1) assigning $b-a$ to $[a,b)$ or $(a,b]$ and infinitesimals to singletons

asked Sep 26, 2012 at 15:21

9 votes

1 answer

698 views

Finitely additive measures on $\mathbb Z_2^\omega$ with invariance and independence constraints

asked May 13, 2014 at 17:51

8 votes

2 answers

335 views

Extending the product measure on $2^\omega$

asked Sep 11, 2017 at 14:57

8 votes

1 answer

1k views

A set of positive measure with cardinality less than that of the continuum?

asked Mar 25, 2013 at 14:37

8 votes

2 answers

351 views

Isometrically-invariant measures and dilation of the Cantor set

asked Sep 27, 2013 at 12:47

6 votes

1 answer

697 views

Is it consistent with ZFC that there is a translation-invariant extension of Lebesgue measure that assigns nonzero measure to some set of measure less than c?

asked Mar 25, 2013 at 20:28

6 votes

1 answer

681 views

Are there uniformly discrete paradoxical subsets in $\mathbb{R}^3$?

asked Jul 14, 2013 at 15:42

6 votes

0 answers

69 views

A sufficient condition for being the boundary of one's convex hull?

asked Feb 12, 2021 at 19:58

6 votes

1 answer

203 views

If a compact convex set meets the positive orthant does it meet it at a point with a normal in the positive orthant?

asked Feb 16, 2021 at 15:38

6 votes

4 answers

576 views

Strength of some claims about finitely additive measures on infinite sets?

asked Nov 13, 2013 at 14:52

6 votes

2 answers

186 views

For most directions does the supporting hyperplane meeting a bounded convex set meet it in one point?

asked Oct 9, 2022 at 17:06

5 votes

1 answer

278 views

Rotation-invariant strict-inclusion-preserving preorderings on subsets of the circle

asked Mar 18, 2013 at 15:11

4 votes

4 answers

1k views

Products of Boolean algebras and probability measures thereon

asked Feb 24, 2013 at 14:47

4 votes

1 answer

183 views

Totally right preorderable groups

asked Nov 6, 2013 at 18:39

4 votes

0 answers

127 views

Self homomorphisms of hyperreals fixing the reals

asked May 9, 2018 at 18:23

3 votes

0 answers

162 views

Random sets and invariant extensions of Lebesgue measure

asked Aug 29, 2017 at 16:39

3 votes

1 answer

926 views

Is an integral against a probability measure in the convex hull of the range?

asked Apr 30, 2014 at 16:48

3 votes

0 answers

204 views

Embedding probability spaces in the completion of $[0,1]^K$

asked Jul 16, 2014 at 21:54

3 votes

1 answer

272 views

Conditional probabilities for all pairs of subsets in $\mathbb R^2$?

asked Jul 7, 2013 at 20:15

3 votes

2 answers

269 views

Hyperfinite set containing the reals, with specified upper bound on internal cardinality?

asked Nov 8, 2012 at 13:47

3 votes

1 answer

236 views

Extending Tarski's Theorem on invariant measures

asked Jul 25, 2013 at 15:56

3 votes

1 answer

284 views

A stronger version of supramenability?

asked Aug 22, 2013 at 14:32

3 votes

1 answer

253 views

Does supramenability imply that $a+c=b+2c \Rightarrow a=b+c$ on the type semigroup?

asked Aug 28, 2013 at 20:13

3 votes

1 answer

208 views

Extensions of partial orders to linear orders on (nonabelian) groups

asked Sep 16, 2013 at 17:18

2 votes

1 answer

203 views

Recovery of probability distribution from a single point

asked May 18, 2013 at 14:05

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40 Questions

Hahn-Banach and the "Axiom of Probabilistic Choice"

How many subsets of $[0,1)$ are there modulo null sets?

Comparing sizes of sets of integers

Full conditional probabilities and versions of AC?

Strength of claims about extensions of partial preorders and orders to linear ones

Hyperreal finitely-additive measure on [0,1) assigning $b-a$ to $[a,b)$ or $(a,b]$ and infinitesimals to singletons

Finitely additive measures on $\mathbb Z_2^\omega$ with invariance and independence constraints

Extending the product measure on $2^\omega$

A set of positive measure with cardinality less than that of the continuum?

Isometrically-invariant measures and dilation of the Cantor set

Is it consistent with ZFC that there is a translation-invariant extension of Lebesgue measure that assigns nonzero measure to some set of measure less than c?

Are there uniformly discrete paradoxical subsets in $\mathbb{R}^3$?

A sufficient condition for being the boundary of one's convex hull?

If a compact convex set meets the positive orthant does it meet it at a point with a normal in the positive orthant?

Strength of some claims about finitely additive measures on infinite sets?

For most directions does the supporting hyperplane meeting a bounded convex set meet it in one point?

Rotation-invariant strict-inclusion-preserving preorderings on subsets of the circle

Products of Boolean algebras and probability measures thereon

Totally right preorderable groups

Self homomorphisms of hyperreals fixing the reals

Random sets and invariant extensions of Lebesgue measure

Is an integral against a probability measure in the convex hull of the range?

Embedding probability spaces in the completion of $[0,1]^K$

Conditional probabilities for all pairs of subsets in $\mathbb R^2$?

Hyperfinite set containing the reals, with specified upper bound on internal cardinality?

Extending Tarski's Theorem on invariant measures

A stronger version of supramenability?

Does supramenability imply that $a+c=b+2c \Rightarrow a=b+c$ on the type semigroup?

Extensions of partial orders to linear orders on (nonabelian) groups

Recovery of probability distribution from a single point