>>16777973
i'm reading about lebesgue integration
the book develops the lebesgue integral using functions that have nondecreasing sequences of step functions that converge almost everywhere and whose sequence of step function integrals is bounded
evidently the difference of two such function is in the space of lebesgue integrable functions

i don't see how this is any different than riemann integration, which was defined in terms of the supremum/infinum of lower/upper sums.

i keep reading that riemann integration proceeds by partitioning the domain, while lebesgue integration proceeds by partitioning the range, which seems to make sense.
but i don't see how this is connected with the development of the lebesgue integral using step functions.

any insights?