Title: Fubini’s nightmare
Speaker: Andrey Gogolyev
Abstract: Fubini’s theorem says that the double integral can be calculated using the integrated integral. In a sense this means that the 2-dimensional Lebesgue measure can be decomposed into 1-dimensional Lebesgue measures. This theorem admits a vast generalization via machinery of measurable partitions and conditional measures due to Rokhlin. I will tell you about this generalized Fubini theorem and the nightmare scenarios when a nice measure such as the Lebesgue measure is being decomposed into atomic measures.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for one or two credit hours of Math 6193 with Professor Nimish Shah.