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Some Measurability Results and Applications to Spaces with Mixed Family-norm

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Abstract

A space with mixed family-norm consists of all functions x on a product space such that the function belongs to V (here, U(t) and V denote given Köthe spaces). Conditions for the measurability of y are given, and the Köthe dual of such spaces is determined. For this purpose a generalization of the Luxemburg-Gribanov theorem for ‘uniformly measurable’ functions is proved. This result is also formulated for vector functions.

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Authors and Affiliations

  1. Department of Mathematics (WE1), Free University of Berlin, Secr. Prof. B. Fiedler Arnimallee 2-6, D-14195, Berlin, Germany

    Martin Väth

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  1. Martin Väth
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Correspondence to Martin Väth.

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The author thanks Y. Abramovich and A. Martellotti for valuable comments and suggestions. This paper was written in the framework of a DFG project (Az. AP 40/15-1). Financial support by the DFG is gratefully acknowledged.

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Väth, M. Some Measurability Results and Applications to Spaces with Mixed Family-norm. Positivity 10, 737–753 (2006). https://doi.org/10.1007/s11117-005-0035-9

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  • DOI: https://doi.org/10.1007/s11117-005-0035-9

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