How subadditive are subadditive capacities?

George L. O'Brien; Wim Vervaat

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 311-324
  • ISSN: 0010-2628

Abstract

top
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).

How to cite

top

O'Brien, George L., and Vervaat, Wim. "How subadditive are subadditive capacities?." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 311-324. <http://eudml.org/doc/247615>.

@article{OBrien1994,
abstract = {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).},
author = {O'Brien, George L., Vervaat, Wim},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {capacities; subadditive capacities; sup measures; hull-additive capacities; vague and narrow topologies; lattice of capacities; sup measures; vague and narrow topologies; lattice of capacities; subadditive capacities; hull-additive capacities},
language = {eng},
number = {2},
pages = {311-324},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {How subadditive are subadditive capacities?},
url = {http://eudml.org/doc/247615},
volume = {35},
year = {1994},
}

TY - JOUR
AU - O'Brien, George L.
AU - Vervaat, Wim
TI - How subadditive are subadditive capacities?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 311
EP - 324
AB - 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).
LA - eng
KW - capacities; subadditive capacities; sup measures; hull-additive capacities; vague and narrow topologies; lattice of capacities; sup measures; vague and narrow topologies; lattice of capacities; subadditive capacities; hull-additive capacities
UR - http://eudml.org/doc/247615
ER -

References

top
  1. Anger B., Lembcke J., Infinitely subadditive capacities as upper envelopes of measures, Z. Wahrsch. theor. verw. Gebiete 68 403-414. Zbl0553.28002MR0771475
  2. Berg C., Christensen J.P.R., Ressel P., Harmonic Analysis on Semigroups, Springer. Zbl0619.43001MR0747302
  3. Choquet G., Theory of capacities, Ann. Inst. Fourier 5 131-295. Zbl0679.01011MR0080760
  4. Choquet G., Lectures on Analysis, Benjamin. Zbl0331.46004
  5. Dellacherie C., Meyer P.A., Probabilities and Potential, Vol. 1, North-Holland. Zbl0716.60001
  6. El Kaabouchi A., Points extrémaux du convexe des mesures majorées par une capacité, C.R. Acad. Sci. Paris 313 37-40. Zbl0777.31009MR1115944
  7. Fuglede B., Capacity as a sublinear functional generalizing an integral, Danske Vid. Selsk. Mat.-Fys. Medd. 38 7. Zbl0222.31002MR0291488
  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. 
  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]. Zbl0883.28002MR1465485
  10. O'Brien G.L., Sequences of capacities, with connections to large deviation theory, Report Dept. Math. Stat. York Univ., to appear. Zbl0847.60061
  11. O'Brien G.L., One-sided limits of capacities, Report Dept. Math. Stat. York Univ., to appear. 
  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. MR1119351
  13. O'Brien G.L., Vervaat W., Capacities and large deviations: an improved toolkit, in preparation. 
  14. Vervaat W., Random upper semicontinuous functions and extremal processes, Report MS-8801, Center for Mathematics and Computer Science, Amsterdam. To appear in [15]. Zbl0882.60003MR1465481
  15. Vervaat W. (editor), Probability and Lattices, CWI Tracts, Center for Math and Comp. Sci., Amsterdam, to appear. MR1465480

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.