## Introductory Real AnalysisSelf-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition. |

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I have read this book from its German translation. That was more understandable. Its English version is like you read and read and read but it's all trivial. You can't get at the point.

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absolutely continuous arbitrary Banach space belongs Borel algebra bounded variation called Clearly closed set closed sphere completely continuous conjugate space contains continuous functions continuous linear functional convex COROLLARY countable set deﬁned deﬁnition denoted elementary set elements equation equivalent Euclidean space Example exists fact ﬁnd ﬁnite number ﬁnite or countable ﬁnite-dimensional follows function deﬁned function f function of bounded given hence Hilbert space implies inequality intersection isomorphic Lebesgue integral Lebesgue measure lemma Let f limit point llfll llxll measurable sets metric space Moreover n-space neighborhood nonempty nonnegative normed linear space obviously one-to-one open intervals open set ordered sets orthogonal orthonormal pairwise disjoint partially ordered positive integers Proof properties Prove real line real numbers rectangles relatively compact satisﬁes scalar product semiring subspace sufﬁciently summable Theorem topological linear space topological space union unique vectors weak topology well-ordered