# A Double Integral Proof

1. Jul 13, 2007

### engin

Show that if f is defined on a rectangle R and double integral of f on R
exists, then f is necessarily bounded on R.

2. Jul 13, 2007

### ObsessiveMathsFreak

If the function is defined on the rectangle the I can't see how it could be unbounded there. Do you mean almost everywhere defined? In the second case, the statement is wrong. Try

$$\int_0^1\int_0^1 \frac{y}{\sqrt{x}}dxdy$$

3. Jul 13, 2007

### mathman

This will be true if you define the integral in terms of ordinary Riemann or Darboux definition. There are more general definitions where boundedness is not required.