Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9502674 | Journal of Mathematical Analysis and Applications | 2005 | 9 Pages |
Abstract
Let Ω={â1,1}N and {Ïj} be independent random variables taking values in {â1,1} 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+aâbâc>0, 1âa+bâc>0 and 1âaâb+c>0. Finite products on Ω, Pn=âj=1n(1+aÏj+bÏj+1+cÏjÏj+1), are studied. We show that the weak limit of {PndÏâ«Î©PndÏ} 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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Qi-Yan Shi,