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In this paper we introduce the - and -convergence and divergence of nets in -groups. We prove some theorems relating different types of convergence/divergence for nets in -group setting, in relation with ideals. We consider both order and -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that -convergence/divergence implies -convergence/divergence for every ideal, admissible for...
Having Polish spaces , and we shall discuss the existence of an -valued random vector such that its conditional distributions satisfy or for some maps , or multifunction respectively. The problem is equivalent to the existence of universally measurable Markov kernel defined implicitly by or respectively. In the paper we shall provide sufficient conditions for the existence of the desired Markov kernel. We shall discuss some special solutions of the - or -problem and illustrate...
Conditions guaranteeing Pettis integrability of a Gelfand integrable multifunction and a decomposition theorem for the Henstock-Kurzweil-Gelfand integrable multifunctions are presented.
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