Integration Theory

W. Filter Professor of Analysis University of Palermo Italy. K. Weber Professor of Mathematics Technikum Winterthur Switzerland.

• 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