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On the Almost Sure Convergence of Floating‐Point Mantissas and Benford's Law

 

作者: Peter Schatte,  

 

期刊: Mathematische Nachrichten  （WILEY Available online 1988）
卷期: Volume 135, issue 1  

页码: 79-83

 

ISSN:0025-584X

 

年代: 1988

 

DOI:10.1002/mana.19881350108

 

出版商: WILEY‐VCH Verlag

 

数据来源: WILEY

 

摘要:

AbstractLetY1,Y2,… be a sequence of random variables and letMnbe the floating‐point mantissa ofYn.Further let 11,x)(·) denote the indicator of the interval (1,x). IfYn/n→Za.s., whereZ≠ 0 is a further random variable, then the sequence 1(1,x)(Mn) converges a.s. to logxin the sense of

 

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