**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)

**Language: **EN