Integration Theory

ISBN-13: 9780412576805 / Angielski / Twarda / 1997 / 294 str.

Opis

The particular strength of this volume is that it unifies the abstract and topological integration theories, and is based on the vector lattice theory which makes many structures more easily understood. It uses the Daniell approach of integrating functions, rather than only measures. This textbook is aimed at undergraduates being introduced to integration theory. Extensive examples and exercises are included.

Spis treści

IntroductionFunction Spaces and FunctionalsOrdered Sets, LatticesThe Spaces RX and R-XVector Lattices of FunctionsFunctionalsDaniell SpacesThe Extension of Daniell SpacesUpper FunctionsLower FunctionsThe Closure of (x, L, I)Convergence of Theorems in (x, L(L), I)ExamplesNull Functions and Null Sets, IntegrabilityExamplesThe Induction PrincipleSummaryMeasure and IntegralThe Extension of Positive Measure SpacesExamplesLocally Integrable FunctionsProduct MeasuresFubini's TheoremMeasures of Hausdorff SpacesLp-SpacesVector Lattices, Lp-SpacesSpaces of MeasuresThe Vector Lattice StructureThe VariationHahn's TheoremAbsolute ContinuityThe Radon-Nikodym TheoremElements of the Theory of Real Functions on RFunctions of Locally Finite VariationAbsolutely Continuous Functions

O autorze

Karl Weber is an author specializing in business, social, and political topics.