The Henstock–Kurzweil Integral [chapter]

Frank Burk
A Garden of Integrals  
In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among which the fact that our integral contains the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one. A.M.S.
more » ... e usual one. A.M.S. SUBJECT CLASSIFICATION (1995): 28B15, 28B05, 28B10, 46G10.
doi:10.7135/upo9781614442097.009 fatcat:mya2kgplunfllkm4okhhcyym6q