Abstract
古典的大數法則是--假設有一串獨立相同分配的隨機變數,則期望值存在時,樣本平均會幾乎收斂到期望值. 1947年,蘇(Hsu)和羅賓斯(Robbins)給了比強大數法則還強的收斂--完全收斂.1949年,俄多士(Erdos)證明蘇(Hsu)和羅賓斯(Robbi)對於動差條件與完全收斂之間的猜想.稍後,1963年凱斯(Katz)考慮完全收斂的速率.我的論文和凱斯的結果一樣,但是條件可以弱一點,不需要獨立;在我的結果中,條件甚至可以是兩兩獨立.The classical law of large number is that when the first momentexists, we know that the sample mean will converge to its mean.Later(1947) Hsu and Robbins defines the convergence which isstronger than the strong law of large number. 1949 Erdos provedHsu and Robbins' conjecture . 1963 Katz consider the rate ofconvergence of smmple mean.In my paper,I obtain the analogousresult as Katz's,but the condition is 2k independent instead oftotally independent.