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 logarithm is a mathematical operation that determines how many times a certain number, called the base, is multiplied by itself to reach another number. Because logarithms relate geometric ...

Let {Sn, n ≥ 1} be a zero, mean square integrable martingale for which $\lim_{n\to\infty}ES_{n}^{2}<\infty$ so that Sn → S∞, a.s., say, by the martingale convergence theorem. The paper is principally ...

Finkelstein's (1971) functional law of the iterated logarithm for empirical distributions is extended to cases where the empirical distribution is multiplied by a ...