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Orthogonally additive functionals on \(BV\). (English) Zbl 1080.46506

Summary: We give a representation theorem for the orthogonally additive functionals on the space \(BV\) in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.

MSC:

46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
26A45 Functions of bounded variation, generalizations
26A39 Denjoy and Perron integrals, other special integrals
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
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