On products of Radon measures

Gryllakis, C. ; Grekas, S.

Fundamenta Mathematicae, Tome 159 (1999), p. 71-84 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 1999-01-01

Zbl 0936.28007

EUDML-ID : urn:eudml:doc:212320

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