# Equality of integrals

1. Jul 6, 2005

### jeanf

i don't know where to start on this problem. could someone help me please? thanks.

let $$f: A -> R$$ be an integrable function, where A is a rectangle. If g = f at all but a finite number of points, show that g is integrable and $$\int_{A}f = \int_{A}g.$$

2. Jul 6, 2005

### Hurkyl

Staff Emeritus
What about g - f?

3. Jul 6, 2005

### lurflurf

Do you mean the Reimann integral? For each value that they are not equal consider a small interval (small enough that only one point of inequality is included). Then |Sup(f)-Sup(g)|=|f(x*)-g(x*)|>0. Then consider the effect of all the points of inequallity on the upper integrals, then likewise for the lower integrals.