Title: What is the Denjoy Integral?
Speaker: Boming Jia
Abstract: Around 1912, the French mathematician Denjoy had trouble understanding integrals like "Integral of (1/x)sin[1/x^3] from 0 to 1." This integral is not a well defined proper Lebesgue integral, so Denjoy developed a new theory of integration to generalize the earlier definition. Decades later, Henstock (1955) and Kurzweil (1957) redefined an equivalent form of the Denjoy Integral by developing (independently) the theory of Gauge Integrals. That definition of integration is “Riemann-like” yet its power is “super-Lebesgue”, as Robert G. Bartle said in his 1996 Monthly paper.
In this talk, I will outline this amazing theory of the Gauge Integral and will share some theorems that could help us appreciate its power.