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2015-04-14 Nonlinear Seminar

dr Giselle Monteiro
New convergence theorem for the abstract Kurzweil-Stieltjes integral

In theory of Riemann integral, the impact of the Bounded Convergence Theorem, also called Arzela or Arzela-Osgood or Osgood Theorem, is comparable to the importance of the Lebesgue Dominated convergence Theorem in the theory of the Lebesgue integration. In this talk we are concerned with the abstract Kurzweil-Stieltjes integral, that is, the Stieltjes type integral for functions with values in a Banach space introduced by S. Schwabik. Our aim is to present the Bounded Convergence Theorem in this general setting.