On the Results of Invariant Sets Under Translation for Probability Measure

Abstract

Probability measure μ의 characteristic 함구가 0이 되는 집합이 유한이면 weakly complete하다는 것이 이미 입증 되었지만 그 결과를 compact 상에서도 성립함을 증명한다.

Let ??(t) denote the Fourier Transorm of probability measure. if s(μ)={t

(t)=0} consists of finitely many elements then μ is weakly complete. We shall show that if S(μ) is compact then μ is weakly complete.

Let ??(t) denote the Fourier Transorm of probability measure. if s(μ)={t

(t)=0} consists of finitely many elements then μ is weakly complete. We shall show that if S(μ) is compact then μ is weakly complete.