A pair of complementary theorems on convergence rates in the law of large numbers
- 1 January 1967
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 63 (1) , 73-82
- https://doi.org/10.1017/s0305004100040901
Abstract
Introduction. Let Xi (i= 1, 2, 3,…) be a sequence of independent and identically distributed random variables with law ℒ(X) and write The Kolmogorov-Marcinkiewicz strong law of large numbers (Loève(6), p. 243) has the following statement:If E|X|r < ∞, then with cr = 0 or EX according as r 1 or r ≥ 1.Keywords
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