Let X1,X2,… be independent random variables with EXk=0 and σk2:=EXk2<∞ (k≥1). Set Sk=X1+⋯+Xk and assume that sk2:=ESk2→∞. We prove that under the Kolmogorov condition |Xn|≤Ln,Ln=o(sn/(loglogsn)1/2)we have 1logsn2&... ...
