## Mathematical AnalysisIt provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis. |

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66 pages matching **Lebesgue integral** in this book

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A classic introduction that is just that.

### Contents

The Real and Complex Number Systems | 1 |

Some Basic Notions of Set Theory | 32 |

Elements of Point Set Topology | 47 |

Copyright | |

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### Common terms and phrases

absolutely convergent accumulation point analytic apply Theorem assume that f axioms bounded variation called Cauchy Cauchy sequence Cauchy-Riemann equations compact interval complex numbers complex-valued function constant contains continuous functions converges absolutely countable collection curve Definition denote differentiable disjoint disk dx exists equation example Exercise f is continuous finite number formula Fourier series function defined function f given Hence implies inequality infinite integer interior point Jacobian Lebesgue integral Let f limit function linear matrix Mean-Value Theorem measure metric space n-ball nonempty nonnegative obtain one-dimensional one-to-one open interval open set partial derivatives partial sums partition positive integers power series properties prove rational numbers real numbers real-valued function Riemann integral Riemann-Stieltjes integral satisfies step functions subinterval theorem shows transformation uniform convergence upper functions variable vector vector-valued function write zero