@inproceedings{d85a9e79ce5942f1a91879f55b2c1297,

title = "Littlewood{\textquoteright}s fourth principle",

abstract = "In real analysis, Littlewood{\textquoteright}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{\textquoteright}s and Egoroff-Severini{\textquoteright}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{\textquoteright}s theorem can be considered as the natural generalization of the classical Dini{\textquoteright}s monotone convergence theorem.",

keywords = "Egorov{\textquoteright}s theorem, Lusin{\textquoteright}s theorem, Measurable finctions",

author = "Rolando Magnanini and Giorgio Poggesi",

year = "2016",

month = aug,

day = "9",

doi = "10.1007/978-3-319-41538-3_9",

language = "English",

isbn = "9783319415369",

volume = "176",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "149--158",

editor = "Carlo Nitsch and Filippo Gazzola and Kazuhiro Ishige and Paolo Salani",

booktitle = "Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s - GPPEPDEs 2015",

address = "Netherlands",

note = "Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE{\textquoteright}s, GPPEPDEs 2015 ; Conference date: 25-05-2015 Through 29-05-2015",

}