  In this paper, we study the summability properties of double sequences of
real constants which map sequences of random variables to sequences of random
variables that are defined on the same probability sample space.
  We show that a regular method of summability is still regular on sequences of
random variables with almost everywhere convergence, almost sure convergence,
and with $L_p$-convergence.
  It is not necessarily regular on sequences of random variables with
convergence in probability.
  We extend these results to random variables with values in extended real
numbers (extended real numbers include infinite values, see definitions 2.2 and
2.3).
  For this we introduce a construction that allows us to multiply sequences of
extended real numbers with infinite real matrices.
