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130626 ||| eng |
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|a 9781461411352
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|a Stroock, Daniel W.
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| 245 |
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|a Essentials of Integration Theory for Analysis
|h Elektronische Ressource
|c by Daniel W. Stroock
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| 250 |
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|a 1st ed. 2011
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| 260 |
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|a New York, NY
|b Springer New York
|c 2011, 2011
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| 300 |
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|a XII, 244 p
|b online resource
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| 653 |
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|a Functions of real variables
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Analysis
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| 653 |
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|a Real Functions
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
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|a Graduate Texts in Mathematics
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| 028 |
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|a 10.1007/978-1-4614-1135-2
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| 856 |
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|u https://doi.org/10.1007/978-1-4614-1135-2?nosfx=y
|x Verlag
|3 Volltext
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|a 515
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|a Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Highlights of this new textbook for the GTM series include revisions to Chapter 1 which add a section about the rate of convergence of Riemann sums and introduces a discussion of the Euler–MacLauren formula. In Chapter 2, where Lebesque’s theory is introduced, a construction of the countably additive measure is done with sufficient generality to cover both Lebesque and Bernoulli measures. Chapter 3 includes a proof of Lebesque’s differential theorem for all monotone functions and the concluding chapter has been expanded to include a proof of Carathéory’s method for constructing measures and his result is applied to the construction of the Hausdorff measures. This new gem is appropriate as a text for a one-semester graduate course in integration theory and is complimented by the addition of several problems related to the new material. The text is also highly useful for self-study. A complete solutions manual is available for instructors who adopt the text for their courses. Additional publications by Daniel W. Stroock: An Introduction to Markov Processes, ©2005 Springer (GTM 230), ISBN: 978-3-540-23499-9; A Concise Introduction to the Theory of Integration, © 1998 Birkhäuser Boston, ISBN: 978-0-8176-4073-6; (with S.R.S. Varadhan) Multidimensional Diffusion Processes, © 1979 Springer (Classics in Mathematics), ISBN: 978-3-540-28998-2
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