Mathematics Graduate Students Organization

Seminar:

Date: October 14

In the development of Fubini's theorem, the monotone class theorem is produced for reasons not initially apparent. The ensuing proofs are invariably cumbersome, and it is rarely explained why such an odd strategy of proof is necessary. In this talk, I'll present a neat result called the lambda-pi theorem, and I will explain how this result can be used, instead of the monotone class theorem, to develop the theory of integration on a product space. Comparing the original proof with this alternative one will provide insight as to the fundamental concept underlying them both. Moreover, while the lambda-pi theorem is weaker than the monotone class theorem, its hypotheses are more lenient. Thus, as we'll see, since the former is sufficient for establishing Fubini's theorem, the alleviated hypotheses accomodate a slightly more efficient proof.