We consider a nontrivial vector space and a semimodular with property: (in other words, is normal (i.e. pregenfunction). The function generates in a metric with
At the same time generates a metric in Musielak-Orlicz sequence space , namely
with . It is proved that the space is complete if and only if the space is complete. We consider also the closed subspace of sequences such that and prove that is separable if and only if is the same. Several examples are...
The notions of metrical and topological vector boundedness of sets are considered in Musielak-Orlicz spaces. The space is called right if both these notions are equivalent. Necessary conditions of the rightness are established, and certain sufficient conditions are found.
Corrections of misprints in the article of I.V. Shragin On a measurability of a superposition, which defines nonlinear integral Musielak operator (Comment. Mathem. Tomus Specialis in honorem Juliani Musialak, Warszawa 2004).
A new proof of some results of V.L. Levin on measurability of projection and on measurable selection is given.
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