Abstract
In this chapter G is a σ-compact locally compact topological group; e is the identity of G; B is the σ-algebra of Borel sets in G and μ l and μ r are fixed left and right Haar measures on G, respectively; λ is a relatively invariant Borel measure on G and Δλ(·) is its modular function; K is the field of all bounded sets in B; K e := {A : e ∈ A ∈ K, μ l (A) > >0} (it is a direction with the following “downwards” order: A l < A 2 if A l ⊃ A 2); M is the set of all Borel measures on G; X = G/K is a left homogeneous space; μ is an invariant measure on X; (⋀, F, P) is a probability space;ℝ̃+=ℝ+∪{+∞}; and ℝ̃=ℝ{-∞}∪{+∞}.
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Bibliographical Notes
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Tempelman, A. (1992). Ergodic Theorems for Homogeneous Random Measures. In: Ergodic Theorems for Group Actions. Mathematics and Its Applications, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1460-0_8
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