Abstract
This chapter discusses probability measures in a metric group. For any two measures μ and ν, the convolution μ* v is defined as the set function μ* ν (α) = ∫ μ (α-1) dν(x), where A ε Bx. The chapter also discusses the properties of the class of all indecomposable measures. A measure λ is said to be decomposable if there exist two nondegenerate measures μ and ν such that λ = μ *ν. In the contrary case, λ is said to be indecomposable. A nondegenerate measure α is said to be a factor of a measure β, if there exists a measure γ such that either β = α*γ or β = γ*α. The chapter also discusses the case when x is abelian.
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