scholarly journals A mean central limit theorem for weakly multiplicative systems and its application to lacunary trigonometric series

1991 ◽  
Vol 89 (2) ◽  
pp. 159-179
Author(s):  
Katusi Fukuyama
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Trigonometric Series ◽  
Central Limit ◽  
Lacunary Trigonometric Series ◽  
Multiplicative Systems

scholarly journals The central limit theorem for trigonometric series

1982 ◽  
Vol 87 ◽  
pp. 79-94 ◽  
Author(s):  
Takafumi Murai
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Trigonometric Series ◽  
Central Limit ◽  
Cardinal Number ◽  
Semi Group ◽  
The Central Limit Theorem ◽  
Positive Integers

We denote by Z+ the semi-group of positive integers. For a subset E of Z+, we denote by |E| (≦ + ∞) its cardinal number and by E(n) the intersection of E and an interval [1, n) (n ≧ 1). We shall identify a subset E of Z+ with a sequence, arranging elements of E according to their order.

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