# Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces

Studia Mathematica (1998)

- Volume: 131, Issue: 3, page 289-302
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topKrupa, G.. "Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces." Studia Mathematica 131.3 (1998): 289-302. <http://eudml.org/doc/216581>.

@article{Krupa1998,

abstract = {Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in $ℝ^d$ are considered. Techniques used here are inspired by [3].},

author = {Krupa, G.},

journal = {Studia Mathematica},

keywords = {multivalued ergodic theorems; measurable multifunctions; random sets; subadditive superstationary processes; set convergence; pointwise and mean ergodic theorems; subadditive superstationary families; random subsets; separable Banach space},

language = {eng},

number = {3},

pages = {289-302},

title = {Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces},

url = {http://eudml.org/doc/216581},

volume = {131},

year = {1998},

}

TY - JOUR

AU - Krupa, G.

TI - Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces

JO - Studia Mathematica

PY - 1998

VL - 131

IS - 3

SP - 289

EP - 302

AB - Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in $ℝ^d$ are considered. Techniques used here are inspired by [3].

LA - eng

KW - multivalued ergodic theorems; measurable multifunctions; random sets; subadditive superstationary processes; set convergence; pointwise and mean ergodic theorems; subadditive superstationary families; random subsets; separable Banach space

UR - http://eudml.org/doc/216581

ER -

## References

top- [1] M. Abid, Un théorème ergodique pour des processus sous-additifs et sur-stationnaires, C. R. Acad. Sci. Paris Sér. A 287 (1978), 149-152. Zbl0386.60028
- [2] Z. Artstein and J. C. Hansen, Convexification in limit laws of random sets in Banach spaces, Ann. Probab. 13 (1985), 307-309. Zbl0554.60022
- [3] E. J. Balder and Ch. Hess, Two generalizations of Komlós' theorem with lower closure-type applications, J. Convex Anal. 3 (1996), 25-44.
- [4] J. Brooks and R. V. Chacon, Continuity and compactness of measures, Adv. Math. 37 (1980), 16-26. Zbl0463.28003
- [5] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977.
- [6] A. Costé, La propriété de Radon-Nikodym en intégration multivoque, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1515-1518. Zbl0313.28007
- [7] A. Costé, Contribution à la théorie de l'intégration multivoque, thèse d'état, Université Pierre et Marie Curie, Paris, 1977.
- [8] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1979.
- [9] J. M. Hammersley, Postulates for subadditive processes, Ann. Probab. 2 (1974), 652-680. Zbl0303.60044
- [10] Ch. Hess, On multivalued martingales whose values may be unbounded: Martingale selectors and Mosco convergence, J. Multivariate Anal. 39 (1991), 175-201. Zbl0746.60051
- [11] F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, ibid. 7 (1977), 149-182. Zbl0368.60006
- [12] J. F. C. Kingman, The ergodic theory of subadditive stochastic processes, J. Roy. Statist. Soc. Ser. B 30 (1968), 499-510. Zbl0182.22802
- [13] U. Krengel, Un théorème ergodique pour les processus sur-stationnaires, C. R. Acad. Sci. Paris Sér. A 282 (1976), 1019-1021. Zbl0343.60017
- [14] K. Schürger, Ergodic theorems for subadditive superstationary families of convex compact random sets, Z. Wahrsch. Verw. Gebiete 62 (1983), 125-135. Zbl0489.60005
- [15] F. A. Valentine, Convex Sets, McGraw-Hill and Wiley, New York, 1968.

## NotesEmbed ?

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