| Title:
|
Semicontinuous integrands as jointly measurable maps (English) |
| Author:
|
Carbonell-Nicolau, Oriol |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
189-193 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Suppose that $(X,\mathcal A)$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $\mathcal A^u$ denote the universal completion of $\mathcal A$. For $x\in X$, let $\underline f(x,\cdot)$ be the lower semicontinuous hull of $f(x,\cdot)$. If $f:X\times Y\rightarrow\overline{\mathbb R}$ is $(\mathcal A^u\otimes\mathcal B(Y),\mathcal B(\overline{\mathbb R}))$-measurable, then $\underline f$ is $(\mathcal A^u\otimes\mathcal B(Y),\mathcal B(\overline{\mathbb R}))$-measurable. (English) |
| Keyword:
|
lower semicontinuous hull |
| Keyword:
|
jointly measurable function |
| Keyword:
|
measurable projection theorem |
| Keyword:
|
normal integrand |
| MSC:
|
28A20 |
| MSC:
|
54C30 |
| idZBL:
|
Zbl 06391536 |
| idMR:
|
MR3193924 |
| . |
| Date available:
|
2014-06-07T15:32:58Z |
| Last updated:
|
2016-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143800 |
| . |
| Reference:
|
[1] Balder E.J.: A general approach to lower semicontinuity and lower closure in optimal control theory.SIAM J. Control Optim. 22 (1984), 570–598. Zbl 0549.49005, MR 0747970, 10.1137/0322035 |
| Reference:
|
[2] Balder E.J.: Generalized equilibrium results for games with incomplete information.Math. Oper. Res. 13 (1988), 265–276. Zbl 0658.90104, MR 0942618, 10.1287/moor.13.2.265 |
| Reference:
|
[3] Balder E.J.: On ws-convergence of product measures.Math. Oper. Res. 26 (2001), 494–518. Zbl 1073.60500, MR 1849882, 10.1287/moor.26.3.494.10581 |
| Reference:
|
[4] Carbonell-Nicolau O., McLean R.P.: On the existence of Nash equilibrium in Bayesian games.mimeograph, 2013. |
| Reference:
|
[5] Cohn D.L.: Measure Theory.Second edition, Birkhäuser/Springer, New York, 2013. Zbl 0860.28001, MR 3098996 |
| Reference:
|
[6] Sainte-Beuve M.-F.: On the extension of von Neumann-Aumann's theorem.J. Functional Analysis 17 (1974), 112–129. Zbl 0286.28005, MR 0374364, 10.1016/0022-1236(74)90008-1 |
| . |
