Title of the course: Henstock-Kurzweil integral
Instructor: Asst. Prof. Serge Randriambololona
Institution: Galatasaray Ü.
Dates: 3-9 September 2018
Prerequisites: A good understanding of a first course of analysis in one variable
Level: Graduate, advanced undergraduate, beginning Undergraduate
Abstract: The Henstock-Kurzweil integral is an integral which is more general than Riemann integral (in the sense that some non Riemann integrable functions may happen to be Henstock-Kurzweil integrable), but does not require measure theory for its definition (as opposed to Lebesgue integral).
We will quickly review the theory of Riemann integral and point-out some of its limitations. We will then discuss how the Henstock-Kurzweil integral allows one to deal with some of these limitations. If time permits, we will discuss some relations to the Lebesgue integral.
Textbook or/and course webpage:
https://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/kurzweil.pdf (part of it)