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Are there any good introductory textbook to cover all these topics?

  1. Jul 8, 2011 #1
    Linear Spaces
    Norms and inner products
    Holder’s inequality
    Minkowski’s inequality
    Normed linear spaces
    Cauchy sequences and complete spaces
    Banach spaces
    Reitz representation theorem
    Hilbert spaces
    Orthogonal bases
    Generalized Fourier expansions

    Lebesgue Measure and Integration
    Sigma fields
    Lebesgue outer measure
    Lebesgue measurability of sets
    Borel sets
    Measurable functions
    Lebesgue’s Theorem
    Egoroff’s Theorem
    Lebesgue Integration
    Bounded convergence theorem
    Fatou’s lemma
    Monotone convergence theorem
    Dominated convergence theorem
    Absolute continuity
  2. jcsd
  3. Jul 8, 2011 #2
    Real analysis by Yeh covers most of these topics very well!
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