On products of Radon measures

Volume 159 / 1999

C. Gryllakis, S. Grekas Fundamenta Mathematicae 159 (1999), 71-84 DOI: 10.4064/fm_1999_159_1_1_71_84


Let $X = [0,1]^Γ$ with card Γ ≥ c (c denotes the continuum). We construct two Radon measures μ,ν on X such that there exist open subsets of X × X which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue product measure: for every finite F ⊆ Γ, the projections of μ and ν onto $[0,1]^F$ are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product measure with the Haar measure.


  • C. Gryllakis
  • S. Grekas

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