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Measure theory and integration

By: Material type: TextTextSeries: Graduate studies in mathematics vol. 76Publication details: 2012 c2006 American Mathematical Society Rhode Island, USADescription: xiii, 319 pISBN:
  • 9780821887189
Subject(s): DDC classification:
  • 515.42 T2M3
Summary: This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to Lp spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to L2 spaces as Hilbert spaces, with a useful geometrical structure. (http://www.universitiespress.com/display.asp?categoryID=0&isbn=978-0-8218-8718-9)
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Item type Current library Item location Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 28-A / Slot 1377 (0 Floor, East Wing) General Stacks 515.42 T2M3 (Browse shelf(Opens below)) Available 176035

This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to Lp spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to L2 spaces as Hilbert spaces, with a useful geometrical structure. (http://www.universitiespress.com/display.asp?categoryID=0&isbn=978-0-8218-8718-9)

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