Littlewood’s fourth principle

Rolando Magnanini, Giorgio Poggesi

Research output: Chapter in Book/Conference paperConference paper

Abstract

In real analysis, Littlewood’s three principles are known as heuristics that help teach the essentials of measure theory and reveal the analogies between the concepts of topological space and continuous function on one side and those of measurable space and measurable function on the other one. They are based on important and rigorous statements, such as Lusin’s and Egoroff-Severini’s theorems, and have ingenious and elegant proofs. We shall comment on those theorems and showhowtheir proofs can possibly bemade simpler by introducing a fourth principle. These alternative proofs make even more manifest those analogies and show that Egoroff-Severini’s theorem can be considered as the natural generalization of the classical Dini’s monotone convergence theorem.

Original languageEnglish
Title of host publicationGeometric Properties for Parabolic and Elliptic PDE’s - GPPEPDEs 2015
EditorsCarlo Nitsch, Filippo Gazzola, Kazuhiro Ishige, Paolo Salani
PublisherSpringer
Pages149-158
Number of pages10
Volume176
ISBN (Print)9783319415369
DOIs
Publication statusPublished - 9 Aug 2016
Externally publishedYes
EventItalian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015 - Palinuro, Italy
Duration: 25 May 201529 May 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume176
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceItalian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015
CountryItaly
CityPalinuro
Period25/05/1529/05/15

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