Example 7.4.4(b): Lebesgue Integral for Simple Functions

Find the Lebesgue integral of a step function, i.e. a function s such that s(x) = cj for xj-1 < x < xj and the { xj } form a partition of [a, b].
Context Context
A step function is a simple function, i.e.
s(x) = cj Xj(x)
where Xj is the characteristic function of the set (xj-1, xj). All sets are measurable with finite measure so that by definition:
s(x) dx = cj m(Xj) = cj (xj - xj-1)
which is again the same answer as for the Riemann integral.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007