Counterexamples in Measure and Integration (Hardcover)

Rene L. Schilling

ISBN 10: 1316519139 / ISBN 13: 9781316519134

Verlag: Cambridge University Press, Cambridge, 2021

Beschreibung

Hardcover. Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to Rene Schilling's other book Measures, Integrals and Martingales . This is a perfect companion to any course on measure theory, integration, real and functional analysis, providing more than 300 examples and counterexamples to the otherwise often rather theoretical courses. By knowing 'what may go wrong' students will gain a better understanding of the standard course material. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Bestandsnummer des Verkäufers 9781316519134

Bibliografische Details

• Titel: Counterexamples in Measure and Integration (Hardcover)
• Verlag: Cambridge University Press, Cambridge
• Erscheinungsjahr: 2021
• Sprache: Englisch
• ISBN-10: 1316519139
• ISBN-13: 9781316519134
• Einband: Hardcover
• Zustand: new

Über diesen Titel

Inhaltsangabe

Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).

Über die Autorinnen und Autoren

René L. Schilling is Professor of Probability Theory at Technische Universität Dresden. His research focuses on stochastic analysis and the theory of stochastic processes.

Franziska Kühn is Research Assistant at Technische Universität Dresden, where she finished her Ph.D. in 2016. She is interested in the interplay of probability theory and analysis, with a focus on jump processes and non-local operators.