I know the standard way to define the integral of a nonnegative measurable function f by using the supremum. How would you do it by taking the infimum?
Here is the question:
Let the nonnegative measurable function f be bounded. Prove that the integral of f under any measurable set A (assume A has finite measure) is the infimum of the set of integrals of simple functions t with f<=t.
Any help would be appreciated!