Pointwise compact sets of measurable functions

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). © 1975 Springer-Verlag.