  The paper deals with the order statistics and empirical mathematical
expectation (which is also called the estimate of mathematical expectation in
the literature) in the case of infinitely increasing random variables. The
Kolmogorov concept which he used in the theory of complexity and the
relationship with thermodynamics which was pointed out already by Poincar\'e
are considered.
  The mathematical expectation (generalizing the notion of arithmetical mean,
which is generally equal to infinity for any increasing sequence of random
variables) is compared with the notion of temperature in thermodynamics by
using an analog of nonstandard analysis.
  The relationship with the Van-der-Waals law of corresponding states is shown.
Some applications of this concept in economics, in internet information
network, and self-teaching systems are considered.
