Is g integrable if it equals f at all but a finite number of points?

[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.

 

[Hurkyl]

What about g - f?

 

[lurflurf]

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.

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.