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Kronecker's lemma : ウィキペディア英語版
Kronecker's lemma
In mathematics, Kronecker's lemma (see, e.g., ) is a result about the relationship between convergence of infinite sums and convergence of sequences. The lemma is often used in the proofs of theorems concerning sums of independent random variables such as the strong Law of large numbers. The lemma is named after the German mathematician Leopold Kronecker.
== The lemma ==
If (x_n)_^\infty is an infinite sequence of real numbers such that
:\sum_^\infty x_m = s
exists and is finite, then we have for 0 and b_n \to \infty that
:\lim_\frac1\sum_^n b_kx_k = 0.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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