Measure and Integral An Introduction to Real Analysis, Second Edition
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- Hardcover ausgewählt
- Taschenbuch
- eBook
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Sprache:Englisch
204,99 €
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
24.04.2015
Abbildungen
8 SW-Abb.
Verlag
Taylor & FrancisSeitenzahl
534
Maße (L/B/H)
24/16,1/3,3 cm
Gewicht
960 g
Auflage
2. Auflage
Sprache
Englisch
ISBN
978-1-4987-0289-8
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less geometric content.
Published nearly forty years after the first edition, this long-awaited Second Edition also:
- Studies the Fourier transform of functions in the spaces L1, L2, and Lp, 1 < p < 2
- Shows the Hilbert transform to be a bounded operator on L2, as an application of the L2 theory of the Fourier transform in the one-dimensional case
- Covers fractional integration and some topics related to mean oscillation properties of functions, such as the classes of Hölder continuous functions and the space of functions of bounded mean oscillation
- Derives a subrepresentation formula, which in higher dimensions plays a role roughly similar to the one played by the fundamental theorem of calculus in one dimension
- Extends the subrepresentation formula derived for smooth functions to functions with a weak gradient
- Applies the norm estimates derived for fractional integral operators to obtain local and global first-order Poincaré-Sobolev inequalities, including endpoint cases
- Proves the existence of a tangent plane to the graph of a Lipschitz function of several variables
- Includes many new exercises not present in the first edition
This widely used and highly respected text for upper-division undergraduate and first-year graduate students of mathematics, statistics, probability, or engineering is revised for a new generation of students and instructors. The book also serves as a handy reference for professional mathematicians.
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