Cantor群上Riesz乘积型测度的奇异性  

Singularity of Riesz product type measure on the Cantor group

作　　者：宋述义[1] 施齐焉[1] 

机构地区：[1]福州大学数学与计算机科学学院,福建福州350108

出　　处：《福州大学学报（自然科学版）》2010年第4期471-475,共5页Journal of Fuzhou University(Natural Science Edition)

摘　　要：研究Riesz型乘积Pn=∏nj=1(1+aωj+bωj+1),其中a,b是满足条件a+b<1的实数,{ωj}是等概率地取值于{-1,1}的独立随机变量.记m为Cantor群Ω={-1,1}∞上的标准哈尔测度,μ为概率测度列Pndω∫Pndω在Ω上弱收敛的唯一一个连续测度,则μ关于m是奇异的.Riesz type products Pn=Пnj=1（1＋aωj＋vωj＋1） are studied, where a, b are two real humbers with ｜ a ｜ ＋ ｜ b｜ 〈 1, and {ωj} are independent random variables taking values in { - 1, 1 } with equal probability. Let m be the normalized Haar measure on the Cantor group Ω={-1,1}^m , and μ be a unique continuous measure that the sequence of probability measures {Pndω/∫ΩPndω} converges weakly on Ω, then μ is singular with respect tom.

关 键 词：Riesz乘积 Cantor群 弱拓扑 奇异性 测度 

分 类 号：O174.2[理学—数学] O174.12[理学—基础数学]