| Title:
|
How subadditive are subadditive capacities? (English) |
| Author:
|
O'Brien, George L. |
| Author:
|
Vervaat, Wim |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
311-324 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic sets). (English) |
| Keyword:
|
capacities |
| Keyword:
|
subadditive capacities |
| Keyword:
|
sup measures |
| Keyword:
|
hull-additive capacities |
| Keyword:
|
vague and narrow topologies |
| Keyword:
|
lattice of capacities |
| MSC:
|
28A05 |
| MSC:
|
28A12 |
| MSC:
|
28C15 |
| idZBL:
|
Zbl 0808.28001 |
| idMR:
|
MR1286578 |
| . |
| Date available:
|
2009-01-08T18:11:15Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118670 |
| . |
| Reference:
|
[1] Anger B., Lembcke J.: Infinitely subadditive capacities as upper envelopes of measures.Z. Wahrsch. theor. verw. Gebiete 68 403-414. Zbl 0553.28002, MR 0771475 |
| Reference:
|
[2] Berg C., Christensen J.P.R., Ressel P.: Harmonic Analysis on Semigroups.Springer. Zbl 0619.43001, MR 0747302 |
| Reference:
|
[3] Choquet G.: Theory of capacities.Ann. Inst. Fourier 5 131-295. Zbl 0679.01011, MR 0080760 |
| Reference:
|
[4] Choquet G.: Lectures on Analysis.Benjamin. Zbl 0331.46004 |
| Reference:
|
[5] Dellacherie C., Meyer P.A.: Probabilities and Potential.Vol. 1, North-Holland. Zbl 0716.60001 |
| Reference:
|
[6] El Kaabouchi A.: Points extrémaux du convexe des mesures majorées par une capacité.C.R. Acad. Sci. Paris 313 37-40. Zbl 0777.31009, MR 1115944 |
| Reference:
|
[7] Fuglede B.: Capacity as a sublinear functional generalizing an integral.Danske Vid. Selsk. Mat.-Fys. Medd. 38 7. Zbl 0222.31002, MR 0291488 |
| Reference:
|
[8] Holwerda H., Vervaat W.: Order and topology in spaces of capacities.preprint. In: Holwerda H., {Topology and Order}, Ph.D. Thesis, Cath. Univ. Nijmegen, 1993. |
| Reference:
|
[9] Norberg T., Vervaat W.: Capacities on non-Hausdorff spaces.Report 1989-11, Dept. Math., Chalmers Univ. Techn. and Univ. Göteborg. To appear in [15]. Zbl 0883.28002, MR 1465485 |
| Reference:
|
[10] O'Brien G.L.: Sequences of capacities, with connections to large deviation theory.Report Dept. Math. Stat. York Univ., to appear. Zbl 0847.60061 |
| Reference:
|
[11] O'Brien G.L.: One-sided limits of capacities.Report Dept. Math. Stat. York Univ., to appear. |
| Reference:
|
[12] O'Brien G.L., Vervaat W.: Capacities, large deviations and loglog laws.in Stable Processes (eds. S. Cambanis, G. Samorodnitsky & M.S. Taqqu), pp. 43-83, Birkhäuser, Boston. MR 1119351 |
| Reference:
|
[13] O'Brien G.L., Vervaat W.: Capacities and large deviations: an improved toolkit.in preparation. |
| Reference:
|
[14] Vervaat W.: Random upper semicontinuous functions and extremal processes.Report MS-8801, Center for Mathematics and Computer Science, Amsterdam. To appear in [15]. Zbl 0882.60003, MR 1465481 |
| Reference:
|
[15] Vervaat W. (editor): Probability and Lattices.CWI Tracts, Center for Math and Comp. Sci., Amsterdam, to appear. MR 1465480 |
| . |
