Real Analysis

Up to my knowledge, this is the only book that constructs the Lebesgue integral for functions to a general Banach-space instead of the real numbers (thus saving us from the unnecessary and esthetically dissapointing construction through positive and negative functions).I don't know how Lang does it, but eerytime you'll pick up one of his books, you'll marvel at the beauty of mathematics ! Real Analysis is designed for a basic graduate course in real analysis. This textbook covers the fundamentals of measure and integration theory, and of functional analysis. The author has incorporated the suggestions of users of the first edition to make this an even more useful textbook for beginning graduate students. This second edition contains many more exercises than the first, including concrete applications of the general theory. As well as the pedagogic treatment of basic material, some topics are treated at a more advanced level, including the spectral theory for unbounded operators, the law of large numbers, and Stokes's Theorem on manifolds. This advanced material also makes the book useful as a reference source. --back cover