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Thickness of a family of sets and uniform measures. (English) Zbl 0651.28002

If S is a set, w a nonempty family of subsets of S, we let \(e(w,S)=\inf_{\lambda}\sup_{W\in w}\lambda (W),\) where \(\lambda\) is a nonnegative function on S, vanishing outside a finite set, summing up its values to 1. Several formulas are given for e(w,S) if every element of S has infinitely many “twins” with respect to w. If this does not hold, it can be “forced” to hold by a trick.
Reviewer: P.Komjáth

MSC:

28A10 Real- or complex-valued set functions
28A12 Contents, measures, outer measures, capacities
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