# On products of Radon measures

Fundamenta Mathematicae (1999)

- Volume: 159, Issue: 1, page 71-84
- ISSN: 0016-2736

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topGryllakis, C., and Grekas, S.. "On products of Radon measures." Fundamenta Mathematicae 159.1 (1999): 71-84. <http://eudml.org/doc/212320>.

@article{Gryllakis1999,

abstract = {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.},

author = {Gryllakis, C., Grekas, S.},

journal = {Fundamenta Mathematicae},

keywords = {product measure problem; Radon measure; Haar measure},

language = {eng},

number = {1},

pages = {71-84},

title = {On products of Radon measures},

url = {http://eudml.org/doc/212320},

volume = {159},

year = {1999},

}

TY - JOUR

AU - Gryllakis, C.

AU - Grekas, S.

TI - On products of Radon measures

JO - Fundamenta Mathematicae

PY - 1999

VL - 159

IS - 1

SP - 71

EP - 84

AB - 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.

LA - eng

KW - product measure problem; Radon measure; Haar measure

UR - http://eudml.org/doc/212320

ER -

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