Proving Lebesgue Integrability for Uniform Limit Step Functions on [0,1]

[pivoxa15]

Homework Statement

If f:[a,b] -> C is the uniform limit of step functions (f_n) on [0,1], show that f is Lebesgue integrable


My first question is why on [0,1] and not on [a,b]?

 

[Dick]

Good question. Must be a typo.