ABSTRACT
The discussion of multiple integration in (Peterson (10) 2020) explains in detail the details for the particular case of Riemann Integration. In this chapter, the author builds Lebesgue measure so the question that remains is how to connect the Lebesgue measure with the product of Lebesgue measure with itself. Expressing this integral in terms of successive single variable integrals leads to the iterated integrals we use to evaluate them in our calculus classes. The author lays out an approximate chain of reasoning to prove our first Fubini result. Pay close attention to how we might have to modify this proof for a more general measure theoretic proof. The author already knows since the outer measure is regular that we can find a measurable cover, but let’s show readers how to construct as it is a nice argument.
