# Lebesgue integral

1. Jan 16, 2010

### katreenaa

Dear all,

Actually, I have question in the attached file about lebesgue integral & I hope to help me plz.

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2. Jan 16, 2010

### JSuarez

$$\frac{1}{1-e^{bx}}=\sum_{n=0}^{\infty}e^{nbx}$$

This will allow you to calculate the integral, in a few properly justified steps.

3. Jan 17, 2010

### katreenaa

Can you explain more plz JSuarez?

4. Jan 17, 2010

### JSuarez

The partial sums of the above series converges monotonically to the function on the right. If you substitute in the in the integral, what do the Lebesgue's convergence theorems tell you about exchanging it with the integral? If that is permissible, you'll have a series with terms that are almost immediate integrals.