Real and complex analysis

  title={Real and complex analysis},
  author={Walter Rudin},
  • W. Rudin
  • Published 1 December 1968
  • Mathematics
Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure… 

Elements of Functional Analysis

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Extensions of Domain Maps in Differential and Integral Calculus

  • A. Edalat
  • Mathematics
    2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
  • 2015
It is proved that the subspace of real-valued continuously differentiable functions on a finite dimensional Euclidean space is dense in the space of Lipschitz maps equipped with the L-topology, and it is shown that the Lebesgue integral operator on integrable functions is the extension of the R-integral operator on continuous functions.

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