The Elements of Integration and Lebesgue Measure

Description

The Elements of Integration and Lebesgue Measure; Contents; The Elements of Integration; 1. Introduction; 2. Measurable Functions; 3. Measures; 4. The Integral; 5. Integrable Functions; 6. The Lebesgue Spaces Lp; 7. Modes of Convergence; 8. Decomposition of Measures; 9. Generation of Measures; 10. Product Measures; The Elements of Lebesgue Measure; 11. Volumes of Cells and Intervals; 12. The Outer Measure; 13. Measurable Sets; 14. Examples of Measurable Sets; 15. Approximation of Measurable Sets; 16. Additivity and Nonadditivity; 17. Nonmeasurable and Non-Borel Sets; References; Index.;The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T.W. Anderson The Statistical Analysis of Time Series T.S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T.J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Rob. The Elements of Integration and Lebesgue Measure Contents The Elements of Integration 1. Introduction 2. Measurable Functions 3. Measures 4. The Integral 5. Integrable Functions 6. The Lebesgue Spaces Lp 7. Modes of Convergence 8. Decomposition of Measures 9. Generation of Measures 10. Product Measures The Elements of Lebesgue Measure 11. Volumes of Cells and Intervals 12. The Outer Measure 13. Measurable Sets 14. Examples of Measurable Sets 15. Approximation of Measurable Sets 16. Additivity and Nonadditivity 17. Nonmeasurable and Non-Borel Sets References Index.