The order structure and topology of the space of measurable functions

Bachelor thesis (2022)

Authors

D. Cohen Electrical Engineering, Mathematics and Computer Science

Contributors

M.C. Veraar Analysis - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2022 Daniel Cohen
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Published Date

28-06-2022

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In probability theory, Lp spaces for p > 0 together with the topology of conver-
gence in probability have been widely applied. However, in that case we restrict
ourselves to only a part of all the measurable functions and to an underlying prob-
ability space. One of the main aims of this thesis is to generalize this concept to
the set of all measurable functions with the usual a.e. equivalence classes (which
we call L0) and (possibly) non-finite measure spaces. The other main aim is to
establish an ordered structure on this L0 space

Files

Order_and_topology_on_L_0.pdf
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