On Mawhin's approach to multiple nonabsolutely convergent integral
Jiří Jarník, Jaroslav Kurzweil, Štefan Schwabik (1983)
Časopis pro pěstování matematiky
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Jiří Jarník, Jaroslav Kurzweil, Štefan Schwabik (1983)
Časopis pro pěstování matematiky
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Štefan Schwabik (1994)
Mathematica Bohemica
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A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].
Štefan Schwabik (1996)
Mathematica Bohemica
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Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. []). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. In [] Ch. S. Honig presented a Stieltjes integral for Banach space valued functions. For Honig’s integral the Dushnik interior...