### Absolute continuity and the Banach-Zaretsky Theorem

- Series
- Analysis Seminar
- Time
- Wednesday, September 29, 2021 - 15:30 for 1 hour (actually 50 minutes)
- Location
- ONLINE (Zoom link in abstract)
- Speaker
- Chris Heil – Georgia Tech – heil@math.gatech.edu

This talk is based on a chapter that I wrote for a book in honor of John Benedetto's 80th birthday. Years ago, John wrote a text "Real Variable and Integration", published in 1976. This was not the text that I first learned real analysis from, but it became an important reference for me. A later revision and expansion by John and Wojtek Czaja appeared in 2009. Eventually, I wrote my own real analysis text, aimed at students taking their first course in measure theory. My goal was that each proof was to be both rigorous and enlightening. I failed (in the chapters on differentiation and absolute continuity). I will discuss the real analysis theorem whose proof I find the most difficult and unenlightening. But I will also present the Banach-Zaretsky Theorem, which I first learned from John's text. This is an elegant but often overlooked result, and by using it I (re)discovered enlightening proofs of theorems whose standard proofs are technical and difficult. This talk will be a tour of the absolutely fundamental concept of absolute continuity from the viewpoint of the Banach-Zaretsky Theorem.

Zoom Link: https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09