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Measure Theory and Integration

A.K. Malik, S.K. Gupta, S.R. Singh, S.C. Malik

ISBN: 9789389698107

INR 345

Description

Integration is one of the two cornerstones of analysis. In the fundamental work of Lebesgue, integration is presented in terms of measure theory. This introductory text starts with the historical development of the notion of the set theory and integral theory. From here, the reader is naturally led to the consideration of the Lebesgue Integral, where abstract integration is developed via the measure theory. The important topics like the Outer Measure, Cantor’s Ternary Set, Measurable Function, the Lebesgue Integral, Fundamental Theorem of Calculus, Lp-spaces, Fubini’s Theorem, the Radon-Nikodym Theorem, and so on are discussed.

  • Countability of Sets
  • Lebesgue Measure
  • Measurable Functions
  • Lebesgue Integral
  • Differentiation and Integration
  • Lp Spaces
  • Product and Signed Measures
  • Appendix: Sets
    References
    Index