Invariant Measures on Coset Spaces
1961 ◽
Vol 5
(2)
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pp. 80-85
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Keyword(s):
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.
1965 ◽
Vol 5
(4)
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pp. 495-505
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Keyword(s):
2018 ◽
Vol 29
(01)
◽
pp. 1850005
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Keyword(s):
1960 ◽
Vol 4
(4)
◽
pp. 208-212
2017 ◽
Vol 60
(1)
◽
pp. 111-121
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Keyword(s):
1974 ◽
Vol 17
(3)
◽
pp. 274-284
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Keyword(s):
Keyword(s):
1999 ◽
Vol 51
(1)
◽
pp. 96-116
◽
Keyword(s):
1981 ◽
Vol 33
(5)
◽
pp. 1097-1110
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Keyword(s):
2007 ◽
Vol 75
(2)
◽
pp. 229-238
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1982 ◽
Vol 33
(1)
◽
pp. 30-39
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