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

Hull Convolution Nite Tame 

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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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