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We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.
It is proved that the Musielak-Orlicz sequence space of Bochner type l_f(X) has property (B) if and only if both spaces lip and X have it also. It is considered the case of Luxemburg and Orlicz norm as well. In particular, the Lebesgue-Bochner sequence space l_p(X) has property (B) iff X has property (B)). As a corollary we also conclude that in Musielak-Orlicz sequence spaces equipped with the Luxemburg...
We introduce the appropriate space of multifunctions and the notions of uniform convexity of some subsets of this space. We get some remarks and theorems on uniform convexity of some subsets of this space. We prove that Musielak-Orlicz space of multifunctions is uniformly convex if the as-sumptions of Theorem 11.6 from [6] hold.
It is considered a Musielak-Orlicz space L generated by a function M:T x X -[0, ] (T is a measure space, X is a topological vector space) and its subspace E of finite elements. The necessary and sufficient conditions are obtained under which L or E contains only the zero function.
The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.
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