## 7.4. Lebesgue Integral

### Example 7.4.4(a): Lebesgue Integral for Simple Functions

The constant function*f(x) = c*can be written as a simple function

Therefore, the (Lebesgue) integral off(x) = c X_{R}(x)

*f*over

*[a, b]*is by definition:

which is the same answer as for the Riemann integral._{[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)