Geodesic
On Multivalued Amarts
Dorota Dudek 1   ; Wiesław Zięba 2
1 Institute of Mathematics Maria Curie-Skłodowska University Pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
2 Institute of Mathematics Maria Curie-Skłodowska University Pl. Marii Curie-Słodowskiej 1 20-031 Lublin, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 93-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space $B$ the fact that every $L^{1}$-bounded $B$-valued martingale converges a.s. in norm to an integrable $B$-valued random variable (r.v.) is equivalent to the Radon–Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.
DOI : 10.4064/ba52-1-10
Keywords: recent years convergence results multivalued functions have developed several areas applied mathematics mathematical economics optimal control mechanics etc note criterion almost sure convergence multivalued asymptotic martingales amarts every separable banach space every bounded b valued martingale converges norm integrable b valued random variable equivalent radon nikodym property paper solve problem convergence multivalued amarts giving topological characterization

Dorota Dudek  1   ; Wiesław Zięba  2

1 Institute of Mathematics Maria Curie-Skłodowska University Pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
2 Institute of Mathematics Maria Curie-Skłodowska University Pl. Marii Curie-Słodowskiej 1 20-031 Lublin, Poland 
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Dorota Dudek; Wiesław Zięba. On Multivalued Amarts. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 1, pp. 93-99. doi: 10.4064/ba52-1-10

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