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Independent Power Measures

  • Colin C. Graham
  • O. Carruth McGehee
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 238)

Abstract

Let G be a locally compact abelian group with dual group Γ and μM(G). The measure μ has independent powers, or μ is i.p., if μmμn whenever 0 ≤ m < n < ∞. The measure μ has strongly independent powers, or μ is strongly i.p., if δ(x)*μ m μ n for 0 ≤m < n < ∞ and all xG. The measure μ is tame if for each ψ ∈ ΔM(G) there exist aC and γ ∈ Γ such that ψ μ = aγ a.e. dμ. The measure μ is monotrochic if for each ψ ∈ ΔM(G) there exists r ∈ [0, 1] such that |ψ μ | = r a.e. dμ. The measure μ is strongly tame or strongly monotrochic if the preceding holds for all ψ ∈ ΔN where N is the L-subalgebra of M(G) generated by μ. The measure μ is Hermitian if \(\tilde{\mu }\) = μ.

Keywords

Probability Measure Haar Measure Finite Subset Compact Subgroup Dual Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Colin C. Graham
    • 1
  • O. Carruth McGehee
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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