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  Record Format   Book  
  Shelf Number   517.518.1 ATH  
  Author   Athreya, Krishna B., 1939-  
  Title   Measure theory / Krishna B. Athreya and Soumendra Lahiri.  
  Imprint   New Delhi : Hindustan, c2006.  
  Collation   xi, 254 pages ;  23 cm.  
  Bibliography Note   Includes bibliographical references and index.  
  Contents   Contents: 1. Measures and Integration: An Informal Introduction -- 2. Measures -- 3. Integration -- 4. L p ­Spaces -- 5. Differentiation -- 6. Product Measures, Convolutions, and Transforms -- 7. Probability Spaces -- A.1 Elementary set theory -- A.2 Real numbers, continuity, differentiability and integration -- A.3 Complex numbers, exponential and trigonometric functions -- A.4 Metric spaces -- A.5 Problems.  
  Description   "This book presents measure and integration theory in a self­contained and step by step manner. After an informal introduction to the subject, the general extension theorem of Caratheodory is presented in Chapter 1. This is followed by the construction of Lebesgue­Stieltjes measures on the real line and Euclidean spaces, and of measures on finite and countable spaces. The presentation gives a general perspective to the subject so as to enable students to think beyond the special, albeit important, example of the Lebesgue measure on the real line. Integration theory is developed in Chapter 2 where the three basic convergence theorems and their extensions are presented. Basic aspects of the theory of Lp, Banach and Hilbert spaces are presented in chapter 3. The Lebesgue­ Radon­Nikodym theorem, signed measures and the fundamental theorem of the Lebesgue integral calculus are taken up in chapter 4. Product measures and their applications to convolutions are discussed in Chapter 5. Also included in Chapter 5 are sections on Fourier Series and Fourier transforms. The last chapter is devoted to basic aspects of probability theory including the Kolmogorov consistency theorem for the construction of stochastic processes. The appendix reviews basic set theory and advanced calculus."--Publisher.  
  Series   Texts and readings in mathematics ; 36  
  Author(s)/Contrib.   Lahiri, S. (Soumendra)  
  Subjects   Integrals -- General.  
    Measure theory.  
  ISBN   9788185931609 paperback  
  Record Number   000112330  
  Digital Object    cover   
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