A scientific calculator has two 'log' buttons on it. These are marked log and ln. The log key is used for calculations of the form \({\log _{10}}x\). For example, to work out that \(\log 10000 = 4\) ...

A law of the iterated logarithm is derived for the empirical distribution functions of a sequence of independent identically distributed random variables. Convergence is in the uniform topology on the ...

A classical result of Philipp (1975) states that for any sequence (n k ) k≥1 of integers satisfying the Hadamard gap condition n k+1 /n k ≥ q > 1 (k = 1, 2,...), the discrepancy D N of the sequence (n ...