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The theory of the Lebesgue integral is a main pillar in the foundation of modern analysis and its applications, including probability theory. This volume shows how and why the Lebesgue integral is such a universal and powerful concept. The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counterexamples are included to show why a hypothesis in a theorem cannot be dropped. The book is based upon a course on real analysis which the author has taught. It is particularly suitable for a one-year course at the graduate level. Precise statements and complete proofs are given for every theorem, with no obscurity left. For this reason the book is also suitable for self-study. Request Inspection Copy
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The surviving examples of the early medieval "shelun," a subgenre of the "fu," are translated and interpreted against their political background in this original contribution to Chinese "Nanbeichao" studies.
Who were the main actors in propagating Christianity in China? Where did Christian communities settle? What discussions were held in China, concerning Christianity? These, and many other, questions are answered in this reference work, which is divided in a systematic part and analytical articles. This handbook represents a true reference guide to the reception of Christianity in pre-1800 China. It presents to the reader, in comprehensive fashion, all current knowledge of Christianity in China, and guides him through the main Chinese and Western sources, bibliographies and archives. The scope of the volume is broad and covers a wide range of topics, such as theology, philosophy, astronomy, mathematics, medicine, cannon, botany, art, music, and more.
This book describes warehouse-scale computers (WSCs), the computing platforms that power cloud computing and all the great web services we use every day. It discusses how these new systems treat the datacenter itself as one massive computer designed at warehouse scale, with hardware and software working in concert to deliver good levels of internet service performance. The book details the architecture of WSCs and covers the main factors influencing their design, operation, and cost structure, and the characteristics of their software base. Each chapter contains multiple real-world examples, including detailed case studies and previously unpublished details of the infrastructure used to powe...