Titlebook: Undergraduate Analysis; Serge Lang Textbook 19831st edition Springer Science+Business Media New York 1983 Analysis.Differentialrechnung.Fo

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Springer Science+Business Media New York 1983

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Limits and Continuous FunctionsLet {..} be a sequence of real numbers. We shall say that the sequence . if there exists an element . ∈ . such that, given ε > 0, there exists a positive integer . such that for all . ≧ . we have

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The Elementary Real IntegralThe proof of the existence of the integral is best postponed until we have the language of normed vector spaces and uniform approximation. However, it is convenient to have the elementary integral available for examples, and exercises, and we need only know its properties, which can be conveniently summarized axiomatically.

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SeriesLet . be a normed vector space. Let{..} be a sequence in ..