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Oct 3, 2020 at 7:01 comment added Anurag Sahay "Theory of Charges: A Study of Finitely Additive Measures" by K.P.S. Bhaskara Rao and M. Bhaskara Rao has a chapter on integration against charges (i.e., against signed finitely additive measures). They cover Dunford-Schwarz's notion of integration in that chapter, along with a different notion of integration which they describe as "of Stieltjes type".
Oct 3, 2020 at 6:30 history answered Martin Väth CC BY-SA 4.0