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Pointwise compact sets of measurable functions

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Abstract

If X is a compact Radon measure space, and A is a pointwise compact set of real-valued measurable functions on X, then A is compact for the topology of convergence in measure (Corollary 2H). Consequently, if Xo,..., Xn are Radon measure spaces, then a separately continuous real-valued function on Xo×X1×...×Xn is jointly measurable (Theorem 3E). If we seek to generalize this work, we encounter some undecidable problems (§4).

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  1. Department of Mathematics, University of Essex, CO4 3SQ, Colchester, England

    D. H. Fremlin

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  1. D. H. Fremlin
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Fremlin, D.H. Pointwise compact sets of measurable functions. Manuscripta Math 15, 219–242 (1975). https://doi.org/10.1007/BF01168675

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