On a Certain Invariant of a Locally Compact Group
نویسنده
چکیده
Group here always means a locally compact Hausdorff group, subgroup means a closed subgroup. Let G be a group, H a subgroup and G/H the locally compact homogeneous space of left cosets x = xH. We denote by $(G) [®(G/H)] the family of all compact subsets of G [G/H], The group G acts on G/H in a natural way. If X C.G and Y QG/H, write XY for the set of all elements xy, x £ I , j £ Y. Now assume that G/H has a nontrivial invariant positive measure dx, e.g. the left invariant Haar measure, if H is normal. For a measurable set U in G/H let | U\ or | U\ G/H be its measure. Then we define:
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