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This introductory text acts as a singular resource for undergraduates learning the fundamental principles and applications of integration theory. Chapters discuss: function spaces and functionals, extension of Daniell spaces, measures of Hausdorff spaces, spaces of measures, elements of the theory of real functions on R.
Introduction Function Spaces and Functionals Ordered Sets, Lattices The Spaces RX and R-X Vector Lattices of Functions Functionals Daniell Spaces The Extension of Daniell Spaces Upper Functions Lower Functions The Closure of (x, L, I) Convergence of Theorems in (x, L(L), I) Examples Null Functions and Null Sets, Integrability Examples The Induction Principle Summary Measure and Integral The Extension of Positive Measure Spaces Examples Locally Integrable Functions Product Measures Fubini's Theorem Measures of Hausdorff Spaces Lp-Spaces Vector Lattices, Lp-Spaces Spaces of Measures The Vector Lattice Structure The Variation Hahn's Theorem Absolute Continuity The Radon-Nikodym Theorem Elements of the Theory of Real Functions on R Functions of Locally Finite Variation Absolutely Continuous Functions
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- ID: 9780412576805
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