Article ID Journal Published Year Pages File Type
9502674 Journal of Mathematical Analysis and Applications 2005 9 Pages PDF
Abstract
Let Ω={−1,1}N and {ωj} be independent random variables taking values in {−1,1} with equal probability. Endowed with the product topology and under the operation of pointwise product, Ω is a compact Abelian group, the so-called Cantor group. Let a,b,c be real numbers with 1+a+b+c>0, 1+a−b−c>0, 1−a+b−c>0 and 1−a−b+c>0. Finite products on Ω, Pn=∏j=1n(1+aωj+bωj+1+cωjωj+1), are studied. We show that the weak limit of {Pndω∫ΩPndω} exists in the topology of M(Ω), where M(Ω) is the convolution algebra of all Radon measure on Ω, thus defined a probability measure on Ω. We also prove that the measure is continuous and singular with respect to the normalized Haar measure on Ω.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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