ABSTRACT
In mathematics and other fields, in this chapter, the author often groups objects of interest into sets and study the properties of these sets. He notes that the sets of measurable and summable functions are closed under scalar multiplication and addition as long as the author interprets addition in the right way when the functions are extended real-valued. The author constructs additional spaces of summable functions. He uses a different notation now to make it clearer the author is thinking of this in the context of measures. The author proves Holder’s and Minkowski’s Inequalities but the proofs, while essentially the same, use a much more abstract point of view.
