Example 7.4.4(a): Lebesgue Integral for Simple Functions

Find the Lebesgue integral of the constant function f(x) = c over the interval [a, b].
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The constant function f(x) = c can be written as a simple function
f(x) = c XR(x)
Therefore, the (Lebesgue) integral of f over [a, b] is by definition:
[a, b] f(x) dx = X[a, b](x) f(x) dx =
      = c X[a, b](x) dx = c m([a, b]) = c (b - a)
which is 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