Open AccessOn the new theory of integration
Author(s) -
William Young
Publication year - 1913
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1913.0016
Subject(s) - mathematical proof , lebesgue integration , monotone polygon , mathematics , riemann hypothesis , calculus (dental) , algebra over a field , pure mathematics , computer science , discrete mathematics , medicine , geometry , dentistry
1. In a paper published in the ' Proceedings of the London Mathematical Society,* addressed to persons already acquainted with Lebesgue integration, I endeavoured to show that the method of monotone sequences enabled us to recognise intuitively the extensibility to Lebesgue integration of results known to be true for Riemann integrals. For this purpose I naturally employed known results in the proofs of Sets of joints ; and, of course, also pre-supposed the proofs of the classical theorems whose generalisation was in question. In the present communication I propose to indicate briefly how the method of monotone sequences enables us to prove, at one and the same time, these theorems and their generalisations. For this purpose we have only to employ a slight modification of the procedure indicated in the paper cited ; one which, however, avoids all reference to the Theory of Sets of Points, and assumes no results whatever in the Theory of Integration.