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  2. List of real analysis topics - Wikipedia

    en.wikipedia.org/wiki/List_of_real_analysis_topics

    Convolution. Cauchy product –is the discrete convolution of two sequences; Farey sequence – the sequence of completely reduced fractions between 0 and 1; Oscillation – is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; and is also a quantitative measure for that.

  3. Littlewood's three principles of real analysis - Wikipedia

    en.wikipedia.org/wiki/Littlewood's_three...

    Littlewood's three principles are quoted in several real analysis texts, for example Royden, [2] Bressoud, [3] and Stein & Shakarchi. [4] Royden [5] gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a ...

  4. Real analysis - Wikipedia

    en.wikipedia.org/wiki/Real_analysis

    The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set ( R {\displaystyle \mathbb {R} } ), together with two binary operations denoted + and ⋅ , and a total order denoted ≤ .

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  6. Glossary of real and complex analysis - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_real_and...

    An Introduction to Complex Analysis in Several Variables. Van Nostrand. Rudin, Walter (1976). Principles of Mathematical Analysis. Walter Rudin Student Series in Advanced Mathematics (3rd ed.). McGraw-Hill. ISBN 9780070542358. Rudin, Walter (1986). Real and Complex Analysis (International Series in Pure and Applied Mathematics). McGraw-Hill.

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  8. Principles of Mathematical Analysis - Wikipedia

    en.wikipedia.org/wiki/Principles_of_Mathematical...

    As a C. L. E. Moore instructor, Rudin taught the real analysis course at MIT in the 1951–1952 academic year. [2] [3] After he commented to W. T. Martin, who served as a consulting editor for McGraw Hill, that there were no textbooks covering the course material in a satisfactory manner, Martin suggested Rudin write one himself.

  9. Category:Real analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Real_analysis

    Real analysis is a traditional division of mathematical analysis, along with complex analysis and functional analysis. It is mainly concerned with the 'fine' (micro-level) behaviour of real functions , and related topics.