Measures equivalent to the Haar measure
Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 157-162
Voir la notice de l'article provenant de la source Cambridge University Press
We call two measures equivalent if each is absolutely continuous with respect to the other (cf. [1]). Let G be a locally compact topological group and let μ be a non-negative Baire measure on G (i.e. μ is denned on all Baire sets, finite on compact sets and positive on open sets). We say that μ is stable if μ (E)=0 implies μ(tE)=0 for each t ∈ G. A. M. Macbeath made the conjecture that every stable non-trivial Baire measure is equivalent to the Haar measure. In this paper we prove the following slightly stronger result:Theorem. Every stable non-trivial measure defined on Baire sets and finite on some open set is equivalent to the Haar measure.
Świerczkowski, S. Measures equivalent to the Haar measure. Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 157-162. doi: 10.1017/S2040618500034092
@article{10_1017_S2040618500034092,
author = {\'Swierczkowski, S.},
title = {Measures equivalent to the {Haar} measure},
journal = {Glasgow mathematical journal},
pages = {157--162},
year = {1960},
volume = {4},
number = {4},
doi = {10.1017/S2040618500034092},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034092/}
}
[1] 1.Halmos, P. R., Measure theory (New York, 1951). Google Scholar
[2] 2.Macbeath, A. M. and Świerczkowski, S., Measures in homogeneous spaces, Fundamenta Math. 49 (1960), 15–24. Google Scholar
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