Multivalued strong laws of large numbers in the slice topology. Application to integrands

Starting from the multivalued strong law of large numbers in the Wijsman topology recently proved by the present author, we deduce two multivalued strong laws of large numbers in the ‘slice topology’ introduced by Beer. An application to integrands via their epigraphical multifunctions is also provided.

[1]  Gerald Beer,et al.  A Polish topology for the closed subsets of a Polish space , 1991 .

[2]  G. Beer.  The slice topology: a viable alternative to Mosco convergence in nonreflexive spaces , 1992 .

[3]  Fumio Hiai,et al.  Convergence of conditional expectations and strong laws of large numbers for multivalued random variables , 1985 .

[4]  F. Hiai,et al.  Integrals, conditional expectations, and martingales of multivalued functions , 1977 .

[5]  Gerald Beer,et al.  On Mosco convergence of convex sets , 1988, Bulletin of the Australian Mathematical Society.

[6]  Loi forte des grands nombres pour des ensembles aléatoires non bornés à valeurs dans un espace de Banach séparable , 1985 .

[7]  Loi de probabilité des ensembles aléatoires à valeurs fermées dans un espace métrique séparable , 1983 .

[8]  U. Mosco.  On the continuity of the Young-Fenchel transform , 1971 .

[9]  Zvi Artstein,et al.  Law of Large Numbers for Random Sets and Allocation Processes , 1981, Math. Oper. Res..

[10]  N. Etemadi.  An elementary proof of the strong law of large numbers , 1981 .

[11]  R. Wijsman.  Convergence of sequences of convex sets, cones and functions. II , 1966 .

[12]  M. Tsukada.  Convergence of best approximations in a smooth Banach space , 1984 .

[13]  R. Wijsman.  Convergence of sequences of convex sets, cones and functions , 1964 .

[14]  Roberto Lucchetti,et al.  Weak topologies for the closed subsets of a metrizable space , 1993 .

[15]  Gerald Beer,et al.  Wijsman convergence of convex sets under renorming , 1994 .

[16]  Constantin Zalinescu,et al.  SET CONVERGENCES. AN ATTEMPT OF CLASSIFICATION , 1993 .