Geodesic
Jacobians for Measures in Coset Spaces
Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 208-212

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a locally compact topological group, let H be a closed subgroup and let G/H be the space of left cosets = xH with the natural topology. We denote by μ a non-negative measure in G/Hdefined on the ring of Baire sets. G acts by left multiplication as a transitive group of homeomorphisms on G/H: Every t ∈ G defines the homeomorphism We write, for E ⊂ G/H, tE = . The measure μ is called stable (cf. [3], [4]) if from t ∈ G, E ⊂ G/H and μ(E) = 0 follows μ(tE) = 0. We say that μ is locally finite [3], [5] if every set of positive measure contains a subset of positive finite measure. 
Świerczkowski, S. Jacobians for Measures in Coset Spaces. Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 208-212. doi: 10.1017/S2040618500034183
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[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 | DOI

[3] 3.Macbeath, A. M. and Świerczkowski, S., Inherited measures; to appear in Proc. Roy. Soc. Edinburgh. Google Scholar

[4] 4.Świerczkowski, S., Measures equivalent to the Haar measure, Proc. Glasgow Math. Assoc., 4 (1960), 157–162. Google Scholar | DOI

[5] 5.Zaanen, A. C., A note on measure theory, Nieuw Arch. Wisk. (3) 6 (1958), 58–65. Google Scholar

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