This text is a single variable real analysis text, designed for the one-year course at the junior, senior, or beginning graduate level. It provides a rigorous and comprehensive treatment of the theoretical concepts of analysis. The book contains most of the topics covered in a text of this nature, but it also includes many topics not normally encountered in comparable texts. These include the Riemann-Stieltjes integral, the Lebesgue integral, Fourier series, the Weiestrass approximation theorem, and an introduction to normal linear spaces. The Real Number System; Sequence Of Real Numbers; Structure Of Point Sets; Limits And Continuity; Differentiation; The Riemann And Riemann-Stieltjes Integral; Series of Real Numbers; Sequences And Series Of Functions; Orthogonal Functions And Fourier Series; Lebesgue Measure And Integration; Logic and Proofs; Propositions and Connectives For all readers interested in real analysis.

1.The real number system 

2.Sequences of real numbers 

3.Structure of point sets 

4.Limits and continuity 

5.Differentiation 

6.The remann and riemann-stieltjes integral 

7.Series of real numbers0

8.Sequences and series of functions 

9.Orthogonal functions and fourier series 

10.Lebesgue measure and integration

Manfred Stoll

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