Measure and integral: an introduction to real analysis/
Wheeden, Richard L.
Measure and integral: an introduction to real analysis/ Richard L. Wheeden [and] Antoni Zygmund. - New York : M. Dekker, c1977. - x, 274 p. : ill. ; 24 cm. - Monographs and textbooks in pure and applied mathematics; 43. .
Includes index.
Preliminaries Points and Sets in RnRn as a Metric SpaceOpen and Closed Sets in Rn: Special SetsCompact Sets; The Heine-Borel TheoremFunctionsContinuous Functions and TransformationsThe Riemann IntegralExercises Function of Bounded Variation; The Riemann-Stieltjes Integral Functions of Bounded VariationRectifiable CurvesThe Reiman-Stieltjes IntegralFurther Results About the Reimann-Stieltjes IntegralsExercises Lebesgue Measure and Outer Measure Lebesgue Outer Measures; The Cantor Set. Lebesgue Measurable SetsTwo Properties of Lebesgue MeasureCharacterizations of MeasurabilityLipschitz Transformations of RnA Nonmeasurable Set. ExercisesLebesgue Measurable Functions Elementary Properties of Measurable Functions. Semicontinuous FunctionsProperties of Measurable Functions; Egorov's Theorem and Lusin's TheoremConvergence in MeasureExercisesThe Lebesgue IntegralDefinition of the Integral of a Nonnegative FunctionProperties of the IntegralThe Integral of an Arbitrary Measurable f A Relation Between Riemann-Stieltjes and Lebesgue Integrals; the LP Spaces, 0
0824764994
Measure theory.
Integrals, Generalized.
515.42 / WHE/M
Measure and integral: an introduction to real analysis/ Richard L. Wheeden [and] Antoni Zygmund. - New York : M. Dekker, c1977. - x, 274 p. : ill. ; 24 cm. - Monographs and textbooks in pure and applied mathematics; 43. .
Includes index.
Preliminaries Points and Sets in RnRn as a Metric SpaceOpen and Closed Sets in Rn: Special SetsCompact Sets; The Heine-Borel TheoremFunctionsContinuous Functions and TransformationsThe Riemann IntegralExercises Function of Bounded Variation; The Riemann-Stieltjes Integral Functions of Bounded VariationRectifiable CurvesThe Reiman-Stieltjes IntegralFurther Results About the Reimann-Stieltjes IntegralsExercises Lebesgue Measure and Outer Measure Lebesgue Outer Measures; The Cantor Set. Lebesgue Measurable SetsTwo Properties of Lebesgue MeasureCharacterizations of MeasurabilityLipschitz Transformations of RnA Nonmeasurable Set. ExercisesLebesgue Measurable Functions Elementary Properties of Measurable Functions. Semicontinuous FunctionsProperties of Measurable Functions; Egorov's Theorem and Lusin's TheoremConvergence in MeasureExercisesThe Lebesgue IntegralDefinition of the Integral of a Nonnegative FunctionProperties of the IntegralThe Integral of an Arbitrary Measurable f A Relation Between Riemann-Stieltjes and Lebesgue Integrals; the LP Spaces, 0
0824764994
Measure theory.
Integrals, Generalized.
515.42 / WHE/M