| Title:
|
Monotone approximation of measurable multifunctions by simple multifunctions (English) |
| Author:
|
Kubiś, Beata |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
113-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets. (English) |
| Keyword:
|
measurable multifunction |
| Keyword:
|
Marczewski function |
| Keyword:
|
Vietoris topology |
| Keyword:
|
simple multifunction |
| MSC:
|
26E25 |
| MSC:
|
28A20 |
| MSC:
|
28B20 |
| MSC:
|
54C60 |
| idZBL:
|
Zbl 0980.28007 |
| idMR:
|
MR1826475 |
| DOI:
|
10.21136/MB.2001.133920 |
| . |
| Date available:
|
2009-09-24T21:47:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133920 |
| . |
| Reference:
|
[1] C. J. Himmelberg: Measurable relations.Fund. Math. 87 (1975), 53–72. Zbl 0296.28003, MR 0367142, 10.4064/fm-87-1-53-72 |
| Reference:
|
[2] B. Kubiś: Approximation of measurable multifunctions.To appear in Tatra Mt. Math. Publ. MR 1771044 |
| Reference:
|
[3] A. Kucia: Some results on Carathéodory selections and extensions.J. Math. Anal. Appl. 223 (1998), 302–318. Zbl 0981.28009, MR 1627308, 10.1006/jmaa.1998.5981 |
| Reference:
|
[4] A. Kucia, A. Nowak: Approximation of Carathéodory type multifunctions.Bull. Polish Acad. Sci. Math. 45 (1997), 187–195. MR 1466844 |
| Reference:
|
[5] E. Marczewski: The characteristic function of a sequence of sets and some of its applications.Fund. Math. 31 (1938), 207–223. |
| Reference:
|
[6] A. Spakowski: On approximation of multifunctions with respect to the Vietoris topology.Acta Univ. Carol. Math. Phys. 29 (1988), 75–80. Zbl 0705.54016, MR 0983453 |
| Reference:
|
[7] A. Spakowski: On approximation by step multifunctions without compactness conditions.Časopis Pěst. Mat. 115 (1990), 225–231. Zbl 0724.54017, MR 1071054 |
| . |
