Sets and integration An outline of the development
Springer Science & Business Media, 6 de des. 2012 - 162 pàgines
The present text resulted from lectures given by the authors at the Rijks Universiteit at Utrecht. These lectures were part of a series on 'History of Contemporary Mathematics'. The need for such an enterprise was generally felt, since the curriculum at many universities is designed to suit an efficient treatment of advanced subjects rather than to reflect the development of notions and techniques. 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. We consider it very useful for a mathematician to have an acquaintance with the history of the development of his subject, especially in the nineteenth century where the germs of many of modern disciplines can be found. Our attention has therefore been mainly directed to relatively young developments. In the lectures we tried to stay clear of both oversimplification and extreme technicality. The result is a text, that should not cause difficulties to a reader with a working knowledge of mathematics. The developments sketched in this book are fundamental for many areas in mathematics and the notions considered are crucial almost everywhere. The book may be most useful, in particular, for those teaching mathematics.
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Sets and Integration An Outline of the Development
D. van Dalen,A. F. Monna
Visualització de fragments - 1972
algebra already analysis Aussonderung axiom of choice axiom of constructibility axiom of foundation axiomatic set theory Baire Borel bounded variation Burali-Forti calculable called Cantor cardinals Cohen concept considered constructive continuous functions continuum hypothesis countable Dedekind defined definition Denjoy denoted dérivée differential domain element ensemble equivalent example existence finite formulated Fraenkel function f geometry Georg Cantor Gödel Grundlagen Heyenoort 61 Hilbert infinity instance interval introduced König Lebesgue Lebesgue measurable Lebesgue-integral Leçons Leibniz logic mapping Math mathematicians mathématique Measurable cardinals measure theory Mengenlehre mention method modern natural numbers Neumann nombre notation notion objects obtained one-one ordered sets ordinals paper paradox Peano Poincaré polyhedrons principle problem proof properties proved real functions real numbers remarks Riemann Riemann-integral second number class sequence set of reals Skolem space subset Tarski theorem topology transfinite urelements valeurs variable well-ordered Zermelo ZF is consistent