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On products of Radon measures

100%

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.

Products of completion regular measures

100%

Fremlin D. H., Grekas S.

Fundamenta Mathematicae

1995

tom 147

nr 1

27-37

We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Grekas S.

1 Fremlin D. H.

1 Gryllakis C.

1 1999

1 1995

Wyniki wyszukiwania

On products of Radon measures

Products of completion regular measures