# Lebesgue integration question

1. May 4, 2010

### AxiomOfChoice

I'm working through some old prelim problems, and one of them has me stumped:

"For $0 < \alpha < \beta < \infty$, for which positive real numbers $p$ do we have

$$\frac{1}{x^\alpha + x^\beta} \in L^p (0,\infty)$$

2. May 4, 2010

### g_edgar

Analyze separately how it behaves near 0 and near infinity.