Timeline for Haar Measure on Locally Compact Semigroups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2014 at 10:56 | comment | added | Benjamin Steinberg | @YemonChoi, people have also studied your variant of an invariant measure. I seem to recall that under minor hypotheses such a measure of global support exists when precisely if you embed in a group, but I am not sure. | |
| Sep 4, 2014 at 2:56 | comment | added | Yemon Choi | That said: for an analyst, the benefit of Haar measure on a LC group is that one can define the L^1 convolution algebra. Now this also works for $R_+$, and $L^1(R_+)$ is a natural object, so perhaps the OP would also be interested in semigroups with measures satisfying the "translates have the same measure" property? | |
| Sep 4, 2014 at 2:52 | comment | added | Yemon Choi | My confusion was that I thought left invariant meant that images under translation had the same measure, rather than inverse images | |
| Sep 4, 2014 at 1:38 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
added 42 characters in body
|
| Sep 4, 2014 at 1:21 | comment | added | Benjamin Steinberg | @YemonChoi, your example is not a counterexample because preimages of Borel sets can change measure. | |
| Sep 4, 2014 at 1:19 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
added 816 characters in body
|
| Sep 4, 2014 at 1:13 | history | undeleted | Benjamin Steinberg | ||
| Sep 4, 2014 at 0:41 | history | deleted | Benjamin Steinberg | via Vote | |
| Sep 4, 2014 at 0:38 | comment | added | Benjamin Steinberg | Maybe this is the result for compact semigroups. Also invariant measure for a semigroup means the measure of the inverse image of a left translation is the same. | |
| Sep 3, 2014 at 23:50 | comment | added | Yemon Choi | What about the positive reals with usual addition and usual topology? | |
| Sep 3, 2014 at 23:17 | history | answered | Benjamin Steinberg | CC BY-SA 3.0 |