A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de. This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).
✔ Author(s): René L. Schilling
✔ Title: Measures, Integrals and Martingales
✔ Rating : 4.8 out of 5 base on (26 reviews)
✔ ISBN-10: 1316620247
✔ ISBN-13: 9781316620243
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Measures, Integrals and Martingales by René L. Schilling
Melody Blake
What a rollercoaster of emotions! I laughed, cried, and everything in between. The author's ability to evoke such raw feelings is truly commendable. It's a story that will stay with me forever.
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The world created in this book was unlike anything I've ever encountered. The author's imagination knows no bounds, and I was completely mesmerized by the fantastical setting.
Daphne Garner
This book is a treasure trove of knowledge and wisdom. The insights offered by the characters and their experiences have left a lasting impression on me.
