A unifying approach to integration for bounded positive charges (Q2470493)

The topic of the paper being reviewed is the integral as a functional and its characteristic, the attempt to produce it under minimal conditions. The language used is however rather unconventional as the authors have an interest in game theory. Thus a bounded, real valued map on an arbitrary set is termed a gamble. Following a first section in which definitions and results from a companion paper are listed, \textit{a general notion of lower integral as an instance of a completely monotone exact functional} is presented and it is shown that a number of existing integrals fit that mold (Riemann, Riemann-Stieltjes, Dunford, Young-Stieltjes, textbook - meaning Halmos et al.). The remainder of the paper explores the immediate scope of the method as well as related matters.