Littlewood's fourth principle
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 continuos 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 show how their proofs can possibly be made simpler by introducing a \textit{fourth principle}. These alternative proofs make even more manifest those analogies and show that Egoroff-Severini's theorem can be considered the natural generalization of the classical Dini's monotone convergence theorem.
Cite
@article{arxiv.1408.0920,
title = {Littlewood's fourth principle},
author = {Rolando Magnanini and Giorgio Poggesi},
journal= {arXiv preprint arXiv:1408.0920},
year = {2014}
}
Comments
11 pages. The paper was stimulated by the remarks by an undergraduate student (GP) during the class "Analisi Matematica III" at the Universit\`a di Firenze. We did not find them in the literature and we thought that they could be interesting for the mathematical community. Comments and suggestions from experts and non-experts are welcome