Timeline for Restriction of Haar measure to Borel $\sigma$ -algebra
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 9, 2011 at 17:06 | vote | accept | arc | ||
| Dec 8, 2011 at 17:18 | answer | added | Gerald Edgar | timeline score: 1 | |
| Dec 8, 2011 at 16:41 | history | edited | arc | CC BY-SA 3.0 |
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| Dec 8, 2011 at 16:35 | history | edited | arc | CC BY-SA 3.0 |
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| Dec 8, 2011 at 2:01 | comment | added | Theo Buehler | Here's a related thread on math.SE: math.stackexchange.com/q/61878 | |
| Dec 8, 2011 at 0:54 | comment | added | Gerald Edgar | Perhaps anyone answering should provide a reference for the particular construction they are using for Haar measure. Even the comments so far seem to be using different ones. | |
| Dec 8, 2011 at 0:22 | comment | added | B R | arc, Haar's theorem is that there is a unique measure satisfying certain properties on the Borel $\sigma$-algebra (a given construction might be defined a-priori on a larger $\sigma$-algebra). Since any measure uniquely extends to its completion, the answer to your question is essentially yes, though you could make the answer be no if you let $M$ be a $\sigma$-algebra strictly containing the completion of $B$ with respect to $\mu|_B$ (since the completion is the smallest complete measure space containing $B$). | |
| Dec 7, 2011 at 23:28 | comment | added | arc | Not necessary. Haar measure is complete, because it is introduced by using Caratheodory theorem, but Borel measure generally is not complete. | |
| Dec 7, 2011 at 23:21 | comment | added | HYL | $M_1$ and $M$ are always the same since Haar mesure is defined on Borel sets. | |
| Dec 7, 2011 at 23:13 | history | edited | arc | CC BY-SA 3.0 |
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| Dec 7, 2011 at 23:04 | comment | added | Asaf Karagila♦ | I have TeXified the post to make it more readable. However the part where you define $\mu_1$ makes little sense, I can guess its meaning, but I don't want to assume too much on the possible contents of your question. | |
| Dec 7, 2011 at 23:03 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
LaTeX.
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| Dec 7, 2011 at 22:55 | history | asked | arc | CC BY-SA 3.0 |