A Note About the Law of the Iteravated Logarithm for independent Random

Let X_i be a sequences of independent random variable with E（X_i） = 0, E（X_i²） ＜ ∞ （i = 1, 2,… ）, where the remainder of the central limit theorem is: △_n＝O((lnBn lnlnBn…(ln_kBn)^1＋δ)^-1), we prove the result as follow:\overline\lim \fracS_n\sqrt2 B_n \ln \ln B_n=1 \quad a.s..