Timeline for On the second dual of $C[0,1]$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 8, 2016 at 11:27 | vote | accept | ABB | ||
| Apr 8, 2016 at 11:11 | comment | added | Simon Henry | I mean't that you should edit your question so that what you have explained to me in the comment appears in the question. In its present form there is no way to understand what you mean by $\psi_{|X}$ as there is no mention of "$X$" in your question, and there is several way to restrict function from $B$ to $[0,1]$. Mentioning that it requires the continuum hypothesis and what is this integral would also be a good things. | |
| Apr 8, 2016 at 11:07 | answer | added | Simon Henry | timeline score: 1 | |
| Apr 8, 2016 at 10:49 | comment | added | ABB | $\psi_{|[0,1]}(t)=\psi(\{t\})$. | |
| Apr 8, 2016 at 10:36 | comment | added | Simon Henry | And what do you mean by "$\psi_{|X}$" ? | |
| Apr 8, 2016 at 10:32 | comment | added | ABB | Yes, Mauldin's result holds under the Continuum Hypothesis. Thanks for your comment. | |
| Apr 8, 2016 at 10:29 | comment | added | ABB | @Simon Henry, Mauldin's paper says that: If $\psi$ and $\mu$ are real valued functions on $B$ then "the number $\omega$ is the integral of $\psi$ with respect to $\mu$" means that if $\epsilon>0$, then there is a subdivision $D$ of $[0,1]$ such that if $D'$ refines $D$, then $$|\sum_{E\in D'} \psi(E)\mu(E)-\omega |\leq \epsilon$$. | |
| Apr 8, 2016 at 10:14 | comment | added | Tomasz Kania | Also, please note that Mauldin's result holds under the Continuum Hypothesis. | |
| Apr 8, 2016 at 9:18 | comment | added | Simon Henry | can you explain what is this integral ? (integrating a function defined on the set of all borel set with respect to a measure ?) Also what do you call $\psi_{|X}$ ? I think the answer to 2. is immediate and has nothing to do with Mauldin result: $V_{\infty}$ is a von neuman algebra in which $C([0,1])$ is weakly dense so it is the quotient of the enveloping algebra (which is isomorphic to the second dual) | |
| Apr 8, 2016 at 8:41 | history | edited | Ian Morris | CC BY-SA 3.0 |
added 1 character in body; edited title
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| Apr 8, 2016 at 8:08 | history | asked | ABB | CC BY-SA 3.0 |