User Julian Newman

47 votes

10 answers

6k views

What is the most "concrete-feeling" equivalent formulation of the Continuum Hypothesis that you can think of?

asked Nov 25, 2023 at 17:09

17 votes

2 answers

1k views

Is it consistent with ZFC that the real line is approachable by sets with no accumulation points?

asked Jun 27 at 15:12

15 votes

1 answer

684 views

Is the topology generated by this weaker notion of a metric necessarily metrisable?

asked Feb 6, 2023 at 22:00

15 votes

1 answer

2k views

Is "conditioning to a sub-$\sigma$-algebra" a measurable operation?

asked Feb 21, 2017 at 17:08

11 votes

3 answers

949 views

Some "axiom of choice" and "dependent choice" issues

asked Sep 21, 2015 at 20:47

10 votes

2 answers

2k views

Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes

asked Aug 16, 2014 at 22:58

10 votes

2 answers

350 views

Is this Riccati equation ("Josephson junction") always phase-locked at integer rotation numbers?

asked Nov 19, 2017 at 16:55

10 votes

2 answers

559 views

Can Birkhoff's ergodic theorem for integrable functions easily be deduced from Birkhoff's ergodic theorem for bounded functions?

asked Oct 21, 2021 at 21:38

9 votes

0 answers

192 views

For measure-preserving systems, is countable generatability of the invariant $\sigma$-algebra equivalent to almost all points being periodic?

asked May 4, 2022 at 22:19

9 votes

0 answers

256 views

Is the inverse of a measurably parametrised family of bijections between standard Borel spaces measurably parametrised?

asked Oct 15, 2019 at 21:53

9 votes

1 answer

873 views

Do the Lebesgue-null sets cover "all the sets can naturally be regarded as sort-of-null sets"?

asked Jun 20, 2017 at 9:00

9 votes

1 answer

604 views

Is it a theorem of ZF that a non-empty countable Cartesian product of finite non-singleton sets has the cardinality of the continuum?

asked Jun 5 at 23:23

8 votes

3 answers

696 views

Is "the purely probabilistic version of Freiling's axiom of symmetry" disprovable in ZFC?

asked Nov 27, 2023 at 12:59

8 votes

3 answers

835 views

Do regular conditional distributions almost surely assign trivial measure to all members of the conditioning $\sigma$-algebra?

asked Aug 11, 2014 at 2:47

7 votes

2 answers

259 views

Can a periodically additively perturbed sinusoidal vector field on the circle have a stable periodic orbit of higher least period?

asked Oct 14, 2017 at 23:15

7 votes

1 answer

309 views

Can the integral of a "generic" bounded measurable function be determined by its values on the rationals?

asked Sep 15, 2015 at 15:31

7 votes

1 answer

882 views

Does the strong Markov property imply the "really strong Markov" property?

asked Feb 21, 2018 at 18:30

6 votes

2 answers

241 views

Does "perpendicular phase incoherence" satisfy the triangle inequality?

asked Oct 31, 2023 at 0:23

6 votes

1 answer

743 views

Which part(s) of this proof of Goodstein's Theorem are not expressible in Peano arithmetic?

asked Jul 2 at 15:43

5 votes

1 answer

254 views

Is the topology of weak+Hausdorff convergence Polish?

asked Jun 24, 2022 at 0:50

5 votes

1 answer

238 views

Is there a name for a "stable" physical measure?

asked Jul 10, 2019 at 16:03

5 votes

0 answers

119 views

Is there a name for a bifurcation where a stable fixed point bifurcates into three fixed points: stable, unstable and saddle?

asked Oct 6, 2015 at 16:40

4 votes

1 answer

131 views

Is every convex subset of a Borel-linearly ordered space measurable?

asked Sep 20, 2015 at 16:39

4 votes

1 answer

244 views

Is it possible for a separable metric and a non-separable metric to have the same Borel $\sigma$-algebra?

asked Aug 10, 2015 at 21:10

4 votes

0 answers

226 views

Does it make sense to regard the graph of any function as being a "sort-of-null set"?

asked Jun 20, 2017 at 15:57

4 votes

1 answer

2k views

Are all linear transformations measurable?

asked Aug 1, 2014 at 5:48

4 votes

1 answer

336 views

Characterising ergodicity of continuous maps

asked Feb 24, 2013 at 0:34

4 votes

1 answer

499 views

Sufficient conditions for a SDE to have a stationary probability measure

asked Jun 9, 2022 at 15:54

4 votes

0 answers

214 views

Can the wavelet bispectrum be normalised so that its integral "gives the right answer"?

asked Feb 23, 2018 at 3:08

4 votes

0 answers

171 views

Convergence of integral formula for Fourier inversion (and Hilbert transform) for integrable piecewise-smooth functions

asked Feb 17, 2018 at 22:45

Stack Exchange Network

89 Questions

What is the most "concrete-feeling" equivalent formulation of the Continuum Hypothesis that you can think of?

Is it consistent with ZFC that the real line is approachable by sets with no accumulation points?

Is the topology generated by this weaker notion of a metric necessarily metrisable?

Is "conditioning to a sub-$\sigma$-algebra" a measurable operation?

Some "axiom of choice" and "dependent choice" issues

Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes

Is this Riccati equation ("Josephson junction") always phase-locked at integer rotation numbers?

Can Birkhoff's ergodic theorem for integrable functions easily be deduced from Birkhoff's ergodic theorem for bounded functions?

For measure-preserving systems, is countable generatability of the invariant $\sigma$-algebra equivalent to almost all points being periodic?

Is the inverse of a measurably parametrised family of bijections between standard Borel spaces measurably parametrised?

Do the Lebesgue-null sets cover "all the sets can naturally be regarded as sort-of-null sets"?

Is it a theorem of ZF that a non-empty countable Cartesian product of finite non-singleton sets has the cardinality of the continuum?

Is "the purely probabilistic version of Freiling's axiom of symmetry" disprovable in ZFC?

Do regular conditional distributions almost surely assign trivial measure to all members of the conditioning $\sigma$-algebra?

Can a periodically additively perturbed sinusoidal vector field on the circle have a stable periodic orbit of higher least period?

Can the integral of a "generic" bounded measurable function be determined by its values on the rationals?

Does the strong Markov property imply the "really strong Markov" property?

Does "perpendicular phase incoherence" satisfy the triangle inequality?

Which part(s) of this proof of Goodstein's Theorem are not expressible in Peano arithmetic?

Is the topology of weak+Hausdorff convergence Polish?

Is there a name for a "stable" physical measure?

Is there a name for a bifurcation where a stable fixed point bifurcates into three fixed points: stable, unstable and saddle?

Is every convex subset of a Borel-linearly ordered space measurable?

Is it possible for a separable metric and a non-separable metric to have the same Borel $\sigma$-algebra?

Does it make sense to regard the graph of any function as being a "sort-of-null set"?

Are all linear transformations measurable?

Characterising ergodicity of continuous maps

Sufficient conditions for a SDE to have a stationary probability measure

Can the wavelet bispectrum be normalised so that its integral "gives the right answer"?

Convergence of integral formula for Fourier inversion (and Hilbert transform) for integrable piecewise-smooth functions