Sequences of Functions : Different Notions of Convergence and How They Are Related

University essay from Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

Author: Erik Sätterqvist; [2018]

Keywords: Sequences of functions; convergence; quasi uniform convergence; Lp-spaces; Funktionsföljder; konvergens; kvasilikformig konvergens; Lp-rum;

Abstract: In this thesis we examine different types of convergence for sequences of functions and how these are related. The functions considered are real valued Lebesgue measurablefunctions defined on a subset of R. We also devote a chapter to explore when continuity of a sequence of functions is preserved under pointwise convergence, and see that this happens precisely when the convergence is quasi uniform.

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