Re: Total Variation

brown042@xxxxxxxxx writes:

Total variation |m| of measure m is defined as |m|(E)= sup (sum of |
m(E_i)|) where the supremum being taken over all countable partitions
{E_i} of E.
How do I show that in this definition countable partitions can be
replaced by finite partitions?

Hint: Given epsilon > 0 and a convergent series S = sum_i s_i, there is
a partial sum > S - epsilon. Given N and a divergent series, there is
a partial sum > N.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.