Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/choice functions.pdf] This note is essentially a rewrite of Appendix V of J. Dixmier’s von Neumann Algebras, North Holland, 1981. The point is to obtain the practical special case: [0.0.1] Corollary: Let X be a locally compact Hausdorff second-countable [1] topological sp...

We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.

amsppt.styFSp90a.tex Pointwise compact and stable sets of measurable functions Introduction In a series of papers culminating in [Ta84], M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the theory of Pettis integration, were solved sub...