MATHEMATICS AND STATISTICS COLLOQUIUM
Leo Livshits, Colby College
What is Measure Theory?
Monday, September 9, 2019
4:00 PM, Davis 301
Refreshments at 3:30 PM, Davis 2nd floor
In December of 1943, few months after being invited to join the Manhattan Project at Los Alamos, Polish American mathematician Stanslaw Ulam published a short article in the American Mathematical Monthly entitled “What is Measure?” There he offered a very a brief account of the developments of a relatively new field of measure theory with some emphasis on the contributions that he had made to it. The article began thus: “The concept of measure includes the notions generalizing the old ideas of length, area, and volume of figures; all of which are among the oldest in mathematics and, in fact, as basic as the idea of number itself.”
As I am offering a course on measure theory this semester, I figured that this may be a good time to give a broader student audience a gentle colloquial overview of the origins and the motivations behind the concept of measure, an area that has since become integral to mathematical analysis. I am borrowing the title from Ulam’s article, because my original more appropriate title attempts of “Why is Measure?” and “How is Measure?” ran into problems with English grammar.
This particular colloquium is aimed at the students, and while the professionals and alike are always welcome to attend, please be warned that the talk will not offer any cutting edge material, and is not designed to impress. On the other hand, I promise the students a number of “wow” moments to illustrate a counterintuitive wonder of the intellectual world that we have created for ourselves.