User Alexander Pruss

8

20

votes

0

answers

370

views

Hahn-Banach and the "Axiom of Probabilistic Choice"

Sep 14 '17 at 16:31 Alexander Pruss 2,047

1

19

votes

2

answers

922

views

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

lebesgue-measure

Mar 22 '15 at 16:47 CommunityBot 1

4

14

votes

1

answer

313

views

Comparing sizes of sets of integers

order-theory

Sep 8 '20 at 0:24 Harry West 1,561

10

votes

0

answers

242

views

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

axiom-of-choice posets reverse-math

Sep 4 '20 at 16:30 Alexander Pruss 2,047

5

10

votes

0

answers

724

views

Full conditional probabilities and versions of AC?

pr.probability set-theory axiom-of-choice boolean-algebras hahn-banach-theorem

Dec 22 '13 at 23:55 user39080 203

4

9

votes

1

answer

664

views

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

pr.probability measure-theory amenability

Aug 29 '18 at 21:01 CommunityBot 1

1

9

votes

2

answers

412

views

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

pr.probability nonstandard-analysis

Sep 27 '12 at 16:56 David Milovich 1,111

8

votes

2

answers

338

views

Isometrically-invariant measures and dilation of the Cantor set

measure-theory fractals hausdorff-dimension

Sep 28 '13 at 5:16 Alexander Pruss 2,047

1

8

votes

1

answer

1k

views

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

measure-theory set-theory

Mar 25 '13 at 14:44 Sean Eberhard 5,613

2

7

votes

1

answer

254

views

Extending the product measure on $2^\omega$

pr.probability measure-theory haar-measure

Sep 13 '17 at 16:23 Alexander Pruss 2,047

2

6

votes

1

answer

144

views

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

convex-geometry

Feb 23 at 14:09 Alexander Pruss 2,047

1

6

votes

0

answers

63

views

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

convex-geometry

Feb 12 at 19:58 Alexander Pruss 2,047

6

votes

1

answer

670

views

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

gr.group-theory measure-theory

Sep 1 '17 at 19:43 YCor 48k

3

6

votes

4

answers

540

views

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

pr.probability set-theory axiom-of-choice reverse-math

Nov 16 '13 at 22:24 Alexander Pruss 2,047

1

6

votes

1

answer

660

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?

measure-theory set-theory

Mar 25 '13 at 21:51 Joseph Van Name 21.3k

1

5

votes

1

answer

274

views

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

pr.probability order-theory linear-orders

Sep 30 '13 at 2:21 Alexander Pruss 2,047

4

votes

1

answer

180

views

Totally right preorderable groups

gr.group-theory order-theory ordered-groups

Feb 16 '20 at 10:29 YCor 48k

1

4

votes

0

answers

122

views

Self homomorphisms of hyperreals fixing the reals

model-theory nonstandard-analysis

May 10 '18 at 14:06 Alexander Pruss 2,047

3

votes

1

answer

195

views

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

gr.group-theory order-theory posets ordered-groups linear-orders

Feb 16 '20 at 20:57 YCor 48k

3

votes

1

answer

244

views

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

gr.group-theory amenability supramenability

Feb 3 '18 at 19:44 Alexander Pruss 2,047

3

votes

0

answers

157

views

Random sets and invariant extensions of Lebesgue measure

measure-theory lebesgue-measure

Aug 31 '17 at 16:41 Alexander Pruss 2,047

3

votes

0

answers

199

views

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

pr.probability measure-theory

Jul 21 '14 at 14:37 Alexander Pruss 2,047

1

3

votes

4

answers

1k

views

Products of Boolean algebras and probability measures thereon

pr.probability ra.rings-and-algebras boolean-algebras

Jul 8 '14 at 15:43 Alexander Pruss 2,047

1

3

votes

1

answer

788

views

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

convexity integration vector-spaces

Apr 30 '14 at 18:18 Alexander Pruss 2,047

2

3

votes

1

answer

269

views

A stronger version of supramenability?

gr.group-theory pr.probability nonstandard-analysis amenability supramenability

Aug 31 '13 at 17:20 Alexander Pruss 2,047

3

votes

1

answer

267

views

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

pr.probability measure-theory

Aug 9 '13 at 2:16 Alexander Pruss 2,047

1

3

votes

1

answer

223

views

Extending Tarski's Theorem on invariant measures

gr.group-theory pr.probability measure-theory

Jul 26 '13 at 5:29 Tyler Bryson 342

3

votes

2

answers

260

views

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

set-theory nonstandard-analysis

Nov 8 '12 at 16:08 Joel David Hamkins 192k

2

votes

1

answer

80

views

Is the support function continuous on its effective domain?

convex-geometry

Mar 2 at 18:25 Alexander Pruss 2,047

1

2

votes

1

answer

203

views

Recovery of probability distribution from a single point

pr.probability

Apr 25 '14 at 6:33 Bjørn Kjos-Hanssen 23.4k

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36 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

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

Full conditional probabilities and versions of AC?

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

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

Isometrically-invariant measures and dilation of the Cantor set

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

Extending the product measure on $2^\omega$

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

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

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

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

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?

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

Totally right preorderable groups

Self homomorphisms of hyperreals fixing the reals

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

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

Random sets and invariant extensions of Lebesgue measure

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

Products of Boolean algebras and probability measures thereon

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

A stronger version of supramenability?

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

Extending Tarski's Theorem on invariant measures

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

Is the support function continuous on its effective domain?

Recovery of probability distribution from a single point