Let G be a locally compact abelian group and M(G) its measure algebra. Two measures μ and λ are said to be equivalent if there exists an invertible measure ϖ such that ϖ*μ = λ. The main result of this note is the following: A measure μ is invertible iff |μ̂| ≥ ε on Ĝ for some ε > 0 and μ is equivalent to a measure λ of the form λ = a + θ, where a ∈ L¹(G) and θ ∈ M(G) is an idempotent measure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-1,
author = {A. \"Ulger},
title = {A characterization of the invertible measures},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {197-203},
zbl = {1184.43002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-1}
}
A. Ülger. A characterization of the invertible measures. Studia Mathematica, Tome 178 (2007) pp. 197-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-1/