Assume $X_i$ has zero mean and unit variance. Define $S_n = \sum_{i=1}^n X_i$.
In the law of large numbers, the quantity $S_n/n$ means sample mean.
In the central limit theorem, the quantity $S_n/\sqrt{n}$ means normalized sample mean to have zero mean and unit variance.
I was wondering what the meaning of the quantity $S_n/\sqrt{n\log\log n}$ in the law of iterated logarithm is?
Thanks!