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On products of Radon measures

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Gryllakis C., Grekas S.

Fundamenta Mathematicae

1999

tom 159

nr 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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Grekas S.

1 Gryllakis C.

1 1999

Wyniki wyszukiwania

On products of Radon measures