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100   $a20130526d1999      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aMeasure, Integral and Probability$b[electronic resource] /$fby Marek Capinski, (Peter) Ekkehard Kopp
205   $a1st ed. 1999.
210  1$aLondon :$cSpringer London :$cImprint: Springer,$d1999.
215   $a1 online resource (XI, 227 p. 20 illus.)
225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085
300   $a"With 23 Figures"--Title page.
311   $a3-540-76260-4 
320   $aIncludes bibliographical references and index.
327   $a1. Motivation and preliminaries -- 2. Measure -- 3. Measurable functions -- 4. Integral -- 5. Spaces of integrable functions -- 6. Product measures -- 7. Limit theorems -- 8. Solutions to exercises -- 9. Appendix -- References.
330   $aThe central concepts in this book are Lebesgue measure and the Lebesgue integral. Their role as standard fare in UK undergraduate mathematics courses is not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications, such as Fourier analysis and the theory of partial differential equations. It follows that not only budding analysts have need of a clear understanding of the construction and properties of measures and integrals, but also that those who wish to contribute seriously to the applications of analytical methods in a wide variety of areas of mathematics, physics, electronics, engineering and, most recently, finance, need to study the underlying theory with some care. We have found remarkably few texts in the current literature which aim explicitly to provide for these needs, at a level accessible to current under­ graduates. There are many good books on modern prob ability theory, and increasingly they recognize the need for a strong grounding in the tools we develop in this book, but all too often the treatment is either too advanced for an undergraduate audience or else somewhat perfunctory.
410  0$aSpringer Undergraduate Mathematics Series,$x1615-2085
606   $aProbabilities
606   $aMathematics
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009
615  0$aProbabilities.
615  0$aMathematics.
615 14$aProbability Theory and Stochastic Processes.
615 24$aMathematics, general.
676   $a515/.42
686   $a60-01$2msc
686   $a28-01$2msc
700   $aCapinski$b Marek$4aut$4http://id.loc.gov/vocabulary/relators/aut$0536472
702   $aKopp$b (Peter) Ekkehard$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910792488403321
996   $aMeasure, integral and probability$91502462
997   $aUNINA