William Johnston: The Lebesgue Integral

Cover: 9781939512079 | The Lebesgue Integral | An Elementary Approach | William Johnston

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Sprache: Englisch

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Beschreibung

Using the Daniell-Riesz approach, this text presents the Lebesgue integral at a level accessible to an audience familiar only with limits, derivatives and series. Employing such minimal prerequisites allows for greatly increased curricular flexibility for course instructors, as well as providing undergraduates with a gateway to the powerful modern mathematics of functions at a very early stage. The book's topics include: the definition and properties of the Lebesgue integral; Banach and Hilbert spaces; integration with respect to Borel measures, along with their associated L2(µ) spaces; bounded linear operators; and the spectral theorem. The text also describes several applications of the theory, such as Fourier series, quantum mechanics, and probability.

Über den Autor

William Johnston is Professor of Mathematics at Butler University, Indiana. His publications include articles on operator theory and functional analysis, and the undergraduate textbooks A Transition to Advanced Mathematics: A Survey Course (with Alex McAllister) and An Introduction to Statistical Inference.

Zusammenfassung

Using the Daniell-Riesz approach, this text presents the Lebesgue integral to an audience familiar only with limits, derivatives and series. Employing such minimal prerequisites allows for increased curricular flexibility for course instructors, and provides undergraduates with a gateway to the modern mathematics of functions at an early stage.

Inhaltsverzeichnis

Preface; Introduction; 1. Lebesgue integrable functions; 2. Lebesgue's integral compared to Riemann's; 3. Functions spaces; 4. Measure theory; 5. Hilbert space operators; Solutions to selected problems; Bibliography.

Erscheinungsjahr:	2015
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	Einband - fest (Hardcover)
ISBN-13:	9781939512079
ISBN-10:	1939512077
Sprache:	Englisch
Einband:	Gebunden
Autor:	Johnston, William
Hersteller:	Mathematical Association of America (MAA)
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	261 x 182 x 22 mm
Von/Mit:	William Johnston
Erscheinungsdatum:	30.09.2015
Gewicht:	0,655 kg

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