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‘Intégrate, longueur, aire’ the centenary of the Lebesgue integral

Published online by Cambridge University Press:  01 August 2016

G. T. Q. Hoare  and
N. J. Lord
G. T. Q. Hoare
Affiliation:
3 Russett Hill, Chalfont St. Peter, Bucks SL9 8JY
N. J. Lord
Affiliation:
Tonbridge School, Kent TN9 1JP
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Extract

‘After Jordan came Lebesgue, and we enter on the subject of another Book’, declared Bourbaki. J.C. Burkill remarked in, ‘It cannot be doubted that (Lebesgue's thesis) is one of the finest which any mathematician has ever written.’ Loève in picturesquely sets the scene for us thus, ‘… the Archimedes of the extension (i.e. modern theory of measure) period was Henri Lebesgue. He took the decisive step in his thesis … . In fact contemporary (measure theory) still dances to Lebesgue's tunes.’ Arguably, before 1902, mathematicians had yet to develop a theory of integration; Lebesgue's great thesis of that year changed this state of affairs irrevocably. In it, difficulties which had begun to plague the Riemannn integral were swept away as Lebesgue boldly extended the concept of the integral by what later came to be regarded as a completion process as profound as that leading from the rational numbers to the reals. Lebesgue created no School but his influence on twentieth century mathematics was profound. In this article celebrating the centenary of Lebesgue's thesis, we look first at Lebesgue's life and then in more detail at his seminal work on integration.

Type
Articles
Information
The Mathematical Gazette , Volume 86 , Issue 505 , March 2002 , pp. 3 - 27
Copyright
Copyright © The Mathematical Association 2002

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