On products of Radon measures

C. Gryllakis; S. Grekas

Fundamenta Mathematicae (1999)

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

Abstract

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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.

How to cite

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Gryllakis, 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 -

References

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