Synopsis The Goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory and Functional Analysis. This book presents a unified treatise of the theory of integration. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading nut also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for research persons.

This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamentals definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis.