an:01295195
Zbl 0936.28007
Gryllakis, C.; Grekas, S.
On products of Radon measures
EN
Fundam. Math. 159, No. 1, 71-84 (1999).
00056624
1999
j
28C05 28C10
product measure problem; Radon measure; Haar measure
Authors' abstract: ``Let \(X= [0,1]^\Gamma\) with \(\text{card }\Gamma\geq{\mathfrak c}\) (\({\mathfrak c}\) denotes the continuum). We construct two Radon measures \(\mu\), \(\nu\) on \(X\) such that there exist open subsets of \(X\times X\) which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue produt measure: for every finite \(F\subseteq \Gamma\), the projections of \(\mu\) and \(\nu\) onto \([0,1]^F\) are equivalent to the \(F\)-dimensional Lebesgue measure. We generalize this construction to any compact group of weight \(\geq{\mathfrak c}\), by replacing the Lebesgue product measure with the Haar measure''.
P.Ressel (Eichst??tt)