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- 0 posts edited
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- 14 votes cast
Sep
24 |
awarded | Autobiographer |
Jul
2 |
awarded | Curious |
Apr
22 |
comment |
Is function from topological group to metric space Borel?
Thanks for your comment. There is something I don't understand. Are you assuming the closure of the identity is not a single point? Is this is necessarily true? |
Apr
22 |
comment |
Is function from topological group to metric space Borel?
Sure. The multiplication of g is a dynamical system, a rotation in a compact abelian group. I want to construct a dynamical isomorphism from a dynamical system in X to G. |
Apr
21 |
comment |
Existence of limit measure
Thanks for your comments. Theorem 4.3 talks about two kinds of limits. The other limit is the outer measure constructed in section 3. Theorem 3.3 mentions that the outer measure is Radon (hence every borel set is measurable) if every open set is the countable union of compact sets. |
Apr
21 |
accepted | Existence of limit measure |
Apr
21 |
asked | Is function from topological group to metric space Borel? |
Apr
20 |
asked | Existence of limit measure |
Mar
4 |
accepted | Extension of measures from the ball sigma-algebra to the borel sigma-algebra |
Feb
28 |
accepted | Weak convergence, and Cesaro convergence (of mu_n (E) ) imply convergence (of mu_n (E))? |
Feb
28 |
asked | Extension of measures from the ball sigma-algebra to the borel sigma-algebra |
Feb
7 |
comment |
Do ergodic isometries have discrete spectrum?
Sure, a theorem by Halmos and Von Neumann state that T is transitive (one dense orbit) and isometric, iff it is topologically isomoprhic to a minimal rotation on a compact abelian group iff T is minimal and has discrete topological spectrum. (topological because in this case the operator associated to the dynamical system is acting on the space of continuous functions. ) A good reference for this is An introduction to ergodic theory by Peter Walters. |
Feb
7 |
asked | Do ergodic isometries have discrete spectrum? |
Nov
12 |
comment |
Weak convergence, and Cesaro convergence (of mu_n (E) ) imply convergence (of mu_n (E))?
Thanks, I was not looking for the case when the cesaro means do not converge. I wanted that as a part of the hypothesis. But I think your counter example works, if you take $x_{n}$=0 only sporadically, then you will have cesaro mean convergence but not convergence. |
Nov
12 |
revised |
Weak convergence, and Cesaro convergence (of mu_n (E) ) imply convergence (of mu_n (E))?
edited tags |
Nov
11 |
awarded | Editor |
Nov
11 |
revised |
Weak convergence, and Cesaro convergence (of mu_n (E) ) imply convergence (of mu_n (E))?
added 34 characters in body |
Nov
9 |
asked | Weak convergence, and Cesaro convergence (of mu_n (E) ) imply convergence (of mu_n (E))? |
Jul
26 |
awarded | Teacher |
Apr
16 |
answered | Proofs that require fundamentally new ways of thinking |