I am studying real analysis now, reading Rudin's book Real and Complex Analysis. One thing confused me is when talking about measurable functions, we assume the function to be, from an abstract space to an abstract space, but when talking about integral, we just integral functions maps into real or complex number field.
Is there any theory about doing integral of functions maps into other adequate algebraic structure, what should I do to learn it? Or any reason only real or complex functions is adequate for integral?
Added: Is there any book recommendation on integral taking value in Banach space?