MR2741185 Talvila, Erik The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219. (Reviewer: Luisa Di Piazza) 46G12 (26A39 46E…

2010

Talvila Erik, The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219, 46Gxx (26A39 46Exx) MR 2 741 185 A descriptive definition of an integral is a definition which provides a ``description'' of the space of primitives. The derivatives in some sense of the primitives are the integrands. In this paper the author introduces a descriptive method of integrating distributions: the regulated primitive integral. The set $\textbf{B}_R= \{F: [-\infty,\infty] \rightarrow {\bf R} \ \ | \mbox{ F {\it is regulated and left continuous on }}\\ \ \ {\bf R}, \ \ F(-\infty)=0, \ \ F(\infty)\in {\bf R}\}$ is the family of primitives. The derivative here is in the sense of the distribu…