Premium
Almost Sure Convergences in the Law of Large Numbers
Author(s) -
Yoneda Kaoru
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004629
Subject(s) - independent and identically distributed random variables , law of large numbers , mathematics , random variable , function (biology) , convergence (economics) , combinatorics , law , discrete mathematics , statistics , political science , economics , evolutionary biology , biology , economic growth
The integrability of a control function of the almost sure convergencelim n → ∞X 1 ( ω ) + X 2 ( ω ) + … + X n ( ω )T n,where T n ↑ ∞ as n → ∞ and X 1 , X 2 , …, X n , … are independent identically distributed random variables, is studied.