Real analysisN.L. Carothers.
Carothers, N. L., 1952-
Real analysisN.L. Carothers. - Cambridge [UK] ; New York : Cambridge University Press, (c)2000. - 1 online resource (xiii, 401 pages) : illustrations.
Includes bibliographies and index.
Metric Spaces -- Calculus Review -- Real Numbers -- Limits and Continuity -- Countable and Uncountable Sets -- Equivalence and Cardinality -- Cantor Set -- Monotone Functions -- Metrics and Norms -- Metric Spaces -- Normed Vector Spaces -- More Inequalities -- Limits in Metric Spaces -- Open Sets and Closed Sets -- Open Sets -- Closed Sets -- Relative Metric -- Continuity -- Continuous Functions -- Homeomorphisms -- Space of Continuous Functions -- Connectedness -- Connected Sets -- Completeness -- Totally Bounded Sets -- Complete Metric Spaces -- Fixed Points -- Completions -- Compactness -- Compact Metric Spaces -- Uniform Continuity -- Equivalent Metrics -- Category -- Discontinuous Functions -- Baire Category Theorem -- Function Spaces -- Sequences of Functions -- Historical Background -- Pointwise and Uniform Convergence -- Interchanging Limits -- Space of Bounded Functions -- Space of Continuous Functions -- Weierstrass Theorem -- Trigonometric Polynomials -- Infinitely Differentiable Functions -- Equicontinuity -- Continuity and Category -- Stone-Weierstrass Theorem -- Algebras and Lattices -- Stone-Weierstrass Theorem -- Functions of Bounded Variation -- Functions of Bounded Variation -- Helly's First Theorem -- Riemann-Stieltjes Integral -- Weights and Measures -- Riemann-Stieltjes Integral -- Space of Integrable Functions -- Integrators of Bounded Variation -- Riemann Integral -- Riesz Representation Theorem -- Other Definitions, Other Properties -- Fourier Series -- Dirichlet's Formula -- Fejer's Theorem -- Complex Fourier Series -- Lebesgue Measure and Integration -- Lebesgue Measure -- Problem of Measure -- Lebesgue Outer Measure -- Riemann Integrability -- Measurable Sets -- Structure of Measurable Sets -- A Nonmeasurable Set -- Other Definitions -- Measurable Functions -- Measurable Functions -- Extended Real-Valued Functions -- Sequences of Measurable Functions -- Approximation of Measurable Functions -- Lebesgue Integral -- Simple Functions -- Nonnegative Functions -- General Case -- Lebesgue's Dominated Convergence Theorem -- Approximation of Integrable Functions -- Additional Topics -- Convergence in Measure -- L[subscript p] Spaces -- Approximation of L[subscript p] Functions -- More on Fourier Series -- Differentiation -- Lebesgue's Differentiation Theorem -- Absolute Continuity
"Aimed at advanced undergraduates and beginning graduate students, Real Analysis offers a rigorous yet accessible course in the subject. Carothers, presupposing only a modest background in real analysis or advanced calculus, writes with an informal style and incorporates historical commentary as well as notes and references." "The book looks at metric and linear spaces, offering an introduction to general topology while emphasizing normed linear spaces. It addresses function spaces and provides familiar applications, such as the Weierstrass and Stone-Weierstrass approximation theorems, functions of bounded variation, Riemann-Stieltjes integration, and a brief introduction to Fourier analysis. Finally, it examines Lebesgue measure and integration on the line. Illustrations and abundant exercises round out the text." "Real Analysis will appeal to students in pure and applied mathematics as well as researchers in statistics, education, engineering, and economics."--BOOK JACKET.
9781139648714
Mathematical analysis.
Electronic Books.
QA300 / .R435 2000
Real analysisN.L. Carothers. - Cambridge [UK] ; New York : Cambridge University Press, (c)2000. - 1 online resource (xiii, 401 pages) : illustrations.
Includes bibliographies and index.
Metric Spaces -- Calculus Review -- Real Numbers -- Limits and Continuity -- Countable and Uncountable Sets -- Equivalence and Cardinality -- Cantor Set -- Monotone Functions -- Metrics and Norms -- Metric Spaces -- Normed Vector Spaces -- More Inequalities -- Limits in Metric Spaces -- Open Sets and Closed Sets -- Open Sets -- Closed Sets -- Relative Metric -- Continuity -- Continuous Functions -- Homeomorphisms -- Space of Continuous Functions -- Connectedness -- Connected Sets -- Completeness -- Totally Bounded Sets -- Complete Metric Spaces -- Fixed Points -- Completions -- Compactness -- Compact Metric Spaces -- Uniform Continuity -- Equivalent Metrics -- Category -- Discontinuous Functions -- Baire Category Theorem -- Function Spaces -- Sequences of Functions -- Historical Background -- Pointwise and Uniform Convergence -- Interchanging Limits -- Space of Bounded Functions -- Space of Continuous Functions -- Weierstrass Theorem -- Trigonometric Polynomials -- Infinitely Differentiable Functions -- Equicontinuity -- Continuity and Category -- Stone-Weierstrass Theorem -- Algebras and Lattices -- Stone-Weierstrass Theorem -- Functions of Bounded Variation -- Functions of Bounded Variation -- Helly's First Theorem -- Riemann-Stieltjes Integral -- Weights and Measures -- Riemann-Stieltjes Integral -- Space of Integrable Functions -- Integrators of Bounded Variation -- Riemann Integral -- Riesz Representation Theorem -- Other Definitions, Other Properties -- Fourier Series -- Dirichlet's Formula -- Fejer's Theorem -- Complex Fourier Series -- Lebesgue Measure and Integration -- Lebesgue Measure -- Problem of Measure -- Lebesgue Outer Measure -- Riemann Integrability -- Measurable Sets -- Structure of Measurable Sets -- A Nonmeasurable Set -- Other Definitions -- Measurable Functions -- Measurable Functions -- Extended Real-Valued Functions -- Sequences of Measurable Functions -- Approximation of Measurable Functions -- Lebesgue Integral -- Simple Functions -- Nonnegative Functions -- General Case -- Lebesgue's Dominated Convergence Theorem -- Approximation of Integrable Functions -- Additional Topics -- Convergence in Measure -- L[subscript p] Spaces -- Approximation of L[subscript p] Functions -- More on Fourier Series -- Differentiation -- Lebesgue's Differentiation Theorem -- Absolute Continuity
"Aimed at advanced undergraduates and beginning graduate students, Real Analysis offers a rigorous yet accessible course in the subject. Carothers, presupposing only a modest background in real analysis or advanced calculus, writes with an informal style and incorporates historical commentary as well as notes and references." "The book looks at metric and linear spaces, offering an introduction to general topology while emphasizing normed linear spaces. It addresses function spaces and provides familiar applications, such as the Weierstrass and Stone-Weierstrass approximation theorems, functions of bounded variation, Riemann-Stieltjes integration, and a brief introduction to Fourier analysis. Finally, it examines Lebesgue measure and integration on the line. Illustrations and abundant exercises round out the text." "Real Analysis will appeal to students in pure and applied mathematics as well as researchers in statistics, education, engineering, and economics."--BOOK JACKET.
9781139648714
Mathematical analysis.
Electronic Books.
QA300 / .R435 2000