Measuring the magnitude of sums
of independent random variables
Department of Mathematics and Computer Science
Philadelphia, PA 19104
Department of Mathematics
University of Missouri-Columbia
Columbia, MO 65211
This paper considers how to measure the magnitude of the sum of
independent random variables in several ways.
We give a formula for the tail distribution for
sequences that satisfy the so called Lévy property.
We then give a connection between the tail distribution and the
th moment, and between the
th moment and
the rearrangement invariant norms.
Keywords: sum of independent random variables,
tail distributions, decreasing rearrangement,
th moment, rearrangement invariant space,
disjoint sum, maximal function,
A.M.S. Classification (1991): Primary 60G50, 60E15, 46E30;