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
✔ 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
Summer Phillips
Delve into a dystopian world where survival hinges on ingenuity and courage. The author's vivid descriptions and fast-paced narrative keep you on the edge of your seat. The protagonist's journey is filled with thrilling moments and unexpected twists. The world-building is detailed and immersive, creating a believable and haunting setting. It's a gripping tale that explores themes of power, resistance, and hope. Ideal for fans of dystopian fiction.
Bets Leonard
Experience the inspiring journey of an individual overcoming incredible odds in this powerful memoir. The author's candid and heartfelt writing brings their story to life. Each chapter reveals the resilience and strength of the human spirit. The narrative is both informative and deeply moving, offering valuable life lessons. It's a story that motivates and inspires, making it a must-read. Perfect for those seeking inspiration and personal growth.
Jaylynn Fernandez
Embark on a journey through time with a historical novel that spans generations. The author's meticulous research and engaging prose create a vivid and immersive experience. Each character's story is intricately woven into the fabric of history. The narrative explores themes of legacy, identity, and change with depth and insight. It's a captivating blend of personal and historical drama. Perfect for fans of multi-generational sagas.
