Geodesic
Invariant Measures on Coset Spaces
Glasgow mathematical journal, Tome 5 (1961) no. 2, pp. 80-85

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

In this note we consider measures on a left coset space G/H, where G is a locally compact group and H is a closed subgroup. We assume the natural topology in G/H and we denote the generic element of this space by xH (x∈G). Every element t∈G defines a homeomorphism of G/H given by t(xH) = (tx)H. A. Weil showed that a Baire measure on G/H invariant under all these homeomorphisms can exist only ifΔ(ξ) = δ(ξ) for each ξ ∈ H,where Δ(x), δ(ξ) denote the modular functions in G, H [6, pp. 42–45]. We shall devote our investigations to inherited measures on G/H (cf. [3] and the definition below) invariant under homeomorphisms belonging to a normal and closed subgroup T ⊂ G. 
Świerczkowski, S. Invariant Measures on Coset Spaces. Glasgow mathematical journal, Tome 5 (1961) no. 2, pp. 80-85. doi: 10.1017/S2040618500034341
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[4] 4.Macbeath, A. M. and Świerczkowski, S., Measures in homogeneous spaces, Fund. Math. 49 (1960), 15–24. Google Scholar | DOI

[5] 5.Macbeath, A. M. and Świerczkowski, S., Limits of lattices in a compactly generated group, Canadian J. Math. 12 (1960), 426–436. Google Scholar | DOI

[6] 6.Weil, A., L'integration dans les groupes topologiques et ses applications (Paris, 1938). Google Scholar

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