Lebesgue Integration and Measure

Häftad, Engelska, 1973

813 kr

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Beskrivning

Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.

Produktinformation

Utgivningsdatum:1973-05-10
Mått:152 x 229 x 17 mm
Vikt:440 g
Format:Häftad
Språk:Engelska
Antal sidor:296
Förlag:Cambridge University Press
ISBN:9780521097512

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

'The book is easy to read, partly because of the treatment adopted, and partly because of the quality of the exposition. Dr Weir's style is clear, friendly and informal; he shows how the results fit in with the reader's intuition; he highlights the important things and warns of the difficult things (these warnings when a hard bit is coming up are most confidence-preserving). He does not aim at maximum generality at the cost of understanding. The examples are chosen with care, many of them being, in effect, lemmas that will be needed later in the proofs of theorems.' Mathematical Gazette

Innehållsförteckning

Preface; 1. The completeness of the reals; 2. Null sets; 3. The Lebesgue integral on R; 4. The Lebesgue integral on Rk; 5. The convergence theorems; 6. Measurable functions and Lebesgue measure; 7. The spaces Lp; Appendix: the elements of topology; Solutions; References; Index.