A version of the law of large numbers
Volume 90 / 2001
Colloquium Mathematicum 90 (2001), 295-298
MSC: 60F15, 42C15.
DOI: 10.4064/cm90-2-9
Abstract
By the method of Rio [10], for a locally square integrable periodic function $f$, we prove $ ( f(\mu _1 ^tx ) + \dots+ f(\mu _n ^tx) )/n \to \int _0^1 f$ for almost every $x$ and $t>0$.
