The Integral à la Henstock -- Part Two

Ponente(s): Peng Yee Lee, Tomás Pérez Becerra

The paper “the integral à la Henstock (2007)” tells a story of the Henstock-Kurzweil integral. In this part two, we go beyond and report the three research tools introduced in the paper. They are: (1) an alternative definition of the Henstock-Kurzweil integral by Zhao Dongsheng, (2) the double Lusin condition, and (3) a definition of Baire one functions. We report on where these tools are being used, and also a link of integration theory with topology and domain theory. In particular, we pose a known problem on the Edalat integral, a computable Riemann integral. The problem is: Is there a corresponding Henstock integral which is computable like the Edalat integral?