| Title:
|
On the extremality of regular extensions of contents and measures (English) |
| Author:
|
Adamski, Wolfgang |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
2 |
| Year:
|
1995 |
| Pages:
|
213-218 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Cal A$ be an algebra and $\Cal K$ a lattice of subsets of a set $X$. We show that every content on $\Cal A$ that can be approximated by $\Cal K$ in the sense of Marczewski has an extremal extension to a $\Cal K$-regular content on the algebra generated by $\Cal A$ and $\Cal K$. Under an additional assumption, we can also prove the existence of extremal regular measure extensions. (English) |
| Keyword:
|
regular content |
| Keyword:
|
lattice |
| Keyword:
|
semicompact |
| Keyword:
|
sequentially dominated |
| MSC:
|
28A12 |
| MSC:
|
46E27 |
| idZBL:
|
Zbl 0834.28001 |
| idMR:
|
MR1357522 |
| . |
| Date available:
|
2009-01-08T18:17:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118749 |
| . |
| Reference:
|
[1] Adamski W.: On regular extensions of contents and measures.J. Math. Anal. Appl. 127 (1987), 211-225. Zbl 0644.28002, MR 0904223 |
| Reference:
|
[2] Adamski W.: On extremal extensions of regular contents and measures.Proc. Amer. Math. Soc. 121 (1994), 1159-1164. Zbl 0817.28002, MR 1204367 |
| Reference:
|
[3] Bierlein D., Stich W.J.A.: On the extremality of measure extensions.Manuscripta Math. 63 (1989), 89-97. Zbl 0663.28004, MR 0975471 |
| Reference:
|
[4] Hackenbroch W.: Measures admitting extremal extensions.Arch. Math. 49 (1987), 257-266. Zbl 0612.28002, MR 0906740 |
| Reference:
|
[5] Lipecki Z.: Components in vector lattices and extreme extensions of quasi-measures and measures.Glasgow Math. J. 35 (1993), 153-162. Zbl 0786.28002, MR 1220557 |
| Reference:
|
[6] Los J., Marczewski E.: Extensions of measure.Fund. Math. 36 (1949), 267-276. Zbl 0039.05202, MR 0035327 |
| Reference:
|
[7] Marczewski E.: On compact measures.Fund. Math. 40 (1953), 113-124. Zbl 0052.04902, MR 0059994 |
| Reference:
|
[8] Pfanzagl J., Pierlo W.: Compact systems of sets.Lecture Notes in Math., Vol. 16, SpringerVerlag, 1966. Zbl 0161.36604, MR 0216529 |
| Reference:
|
[9] Plachky D.: Extremal and monogenic additive set functions.Proc. Amer. Math. Soc. 54 (1976), 193-196. Zbl 0285.28005, MR 0419711 |
| Reference:
|
[10] Schwartz L.: Radon measures on arbitrary topological spaces and cylindrical measures.Oxford UP, 1973. Zbl 0298.28001, MR 0426084 |
| Reference:
|
[11] von Weizsäcker H.: Remark on extremal measure extensions.Lecture Notes in Math., Vol. 794, Springer-Verlag, 1980. MR 0577962 |
| . |
