I’ve been always told that Kolmogorov firstly proved the law of iterated logarithm (LIL). One day I happened to have a look at his original piece of the proof of LIL, and happily found that it was not written in Russian. When I was reading Kolmogorov’s piece, I had a hard time to figure out some random jumps in the proof. By seeking for help in the reference papers, I found Khintchine’s paper, from which Kolmogorove borrowed some ideas.
Actually Khintchine’s paper is the first paper which stated and proved the law of iterated logarithm, but for a special case – a series of bernoulli distribution random variables. Kolmogorov generalized his idea to bounded random variables.
The translation of Khintchine’s paper as a weekend activity 😛 : Uber einen satz der wahrscheinlichkeitsrechnung (English Translation)