# Lebesgue integral

1. Dec 7, 2005

### eljose

let be the Lebesgue integral with a meassure $$\mu$$ then if we call this integral..

$$\int_{X}fd\mu=I$$

my questions are..how would you calculate the integral of f(x)=exp(x) from 1 to 10?..another question let be the lebesgue integral on the interval X=(0,t) would be true that:

$$(\frac{d}{dt}\int_{X}fd\mu=f(t)$$?

thanks...

Last edited: Dec 7, 2005
2. Dec 7, 2005

### HallsofIvy

The same way you would a Riemann integral. If a function is Riemann integrable on an interval, then it is Lebesque integrable on that interval and the two integrals are the same.

Except possibly on a set of measure 0, yes.

3. Dec 7, 2005

### mathwonk

you need some hypotheses of course, but if f is "summable" then it is the derivative a.e. of its indefinite integral. see pages 11 and 47, 48 of Riesz Nagy.