On products of Radon measures

• Autorzy: C. Gryllakis , S. Grekas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 159
• Numer: 1
• Strony: 71-84

Daty

wydano

1999

otrzymano

1997-09-12

Twórcy

autor

C. Gryllakis

• Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece

autor

S. Grekas

• Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece

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