عنوان

Measure and integral :

1498702902

1498702910

149870302X

9781498702904

9781498702911

9781498703024

b544989

Measure and integral :

[Book]

an introduction to real analysis

Richard L. Wheeden.

Second edition

Boca Raton

Chapman & Hall/CRC

2015

: illustrations (black and white).

Chapman & Hall/CRC pure and applied mathematics, 308

Preface to the Second Edition Preface to the First Edition Authors Preliminaries Points and Sets in Rn Rn as a Metric Space Open and Closed Sets in Rn,

Preface to the Second EditionPreface to the First EditionAuthorsPreliminariesPoints and Sets in RnRn as a Metric SpaceOpen and Closed Sets in Rn, and Special SetsCompact Sets and the Heine-Borel TheoremFunctionsContinuous Functions and TransformationsThe Riemann IntegralExercisesFunctions of Bounded Variation and the Riemann-Stieltjes IntegralFunctions of Bounded VariationRectifiable CurvesThe Riemann-Stieltjes IntegralFurther Results about Riemann-Stieltjes IntegralsExercisesLebesgue Measure and Outer MeasureLebesgue Outer Measure and the Cantor SetLebesgue Measurable SetsTwo Properties of Lebesgue MeasureCharacterizations of MeasurabilityLipschitz Transformations of RnA Nonmeasurable SetExercisesLebesgue Measurable FunctionsElementary Properties of Measurable FunctionsSemicontinuous FunctionsProperties of Measurable Functions and Theorems of Egorov and LusinConvergence in MeasureExercisesThe Lebesgue IntegralDefinition of the Integral of a Nonnegative FunctionProperties of the IntegralThe Integral of an Arbitrary Measurable fRelation between Riemann-Stieltjes and Lebesgue Integrals, and the Lp Spaces, 0 < p < Riemann and Lebesgue IntegralsExercisesRepeated IntegrationFubini's TheoremTonelli's TheoremApplications of Fubini's TheoremExercisesDifferentiationThe Indefinite IntegralLebesgue's Differentiation TheoremVitali Covering LemmaDifferentiation of Monotone FunctionsAbsolutely Continuous and Singular FunctionsConvex FunctionsThe Differential in RnExercisesLp ClassesDefinition of LpHoelder's Inequality and Minkowski's InequalityClasses l pBanach and Metric Space PropertiesThe Space L2 and OrthogonalityFourier Series and Parseval's FormulaHilbert SpacesExercisesApproximations of the Identity and Maximal FunctionsConvolutionsApproximations of the IdentityThe Hardy-Littlewood Maximal FunctionThe Marcinkiewicz IntegralExercisesAbstract IntegrationAdditive Set Functions and MeasuresMeasurable Functions and IntegrationAbsolutely Continuous and Singular Set Functions and MeasuresThe Dual Space of LpRelative Differentiation of MeasuresExercisesOuter Measure and MeasureConstructing Measures from Outer MeasuresMetric Outer MeasuresLebesgue-Stieltjes MeasureHausdorff MeasureCaratheodory-Hahn Extension TheoremExercisesA Few Facts from Harmonic AnalysisTrigonometric Fourier SeriesTheorems about Fourier CoefficientsConvergence of S[f] and STH[f]Divergence of Fourier SeriesSummability of Sequences and SeriesSummability of S[f] and STH[f] by the Method of the Arithmetic MeanSummability of S[f] by Abel MeansExistence of f THProperties of f TH for f Lp, 1 < p < Application of Conjugate Functions to Partial Sums of S[f]ExercisesThe Fourier TransformThe Fourier Transform on L1The Fourier Transform on L2The Hilbert Transform on L2The Fourier Transform on Lp, 1 < p < 2ExercisesFractional IntegrationSubrepresentation Formulas and Fractional IntegralsL1, L1 Poincare Estimates and the Subrepresentation Formula; Hoelder ClassesNorm Estimates for I Exponential Integrability of I fBounded Mean OscillationExercisesWeak Derivatives and Poincare-Sobolev EstimatesWeak DerivativesApproximation by Smooth Functions and Sobolev SpacesPoincare-Sobolev EstimatesExercisesNotationsIndex

Integrals, Generalized.

Measure theory.

Richard L. Wheeden.

Richard L Wheeden

[Book]

Y