Sets and integration : an outline of the development.
As it is very likely that this trend will continue, we decided to offer lectures of a less technical nature to provide students and interested listeners with a survey of the history of topics in our present-day mathematics.
viii, 162 p. : il. ; 25 cm
9789001597757, 9001597750
850846830
Set theory from Cantor to Cohen.- Forebodings.- The exploration of the new continent.- The paradoxes.- The axiom of choice.- Zermelo takes over.- Making inconsistent sets respectable.- The consistency of the axiom of choice and the continuum hypothesis.- The independence of the continuum hypothesis.- Large cardinals.- Games and strategies.- The integral from Riemann to Bourbaki.- Introduction; the period before Riemann.- Greek mathematics.- Seventeenth century.- Leibniz and Newton.- Riemann, Lebesgue, real functions.- Riemann.- Measure theory.- Lebesgue.- More about Lebesgue.- Controversies.- Real functions.- Denjoy.- Perron.- Further developments.- Modern theory of the integral.- Integrals as linear functions.- Generalizations.- Carathéodory.- Haar-measure.- List of Mathematicians.