Ebook: Introduction to modern analysis

This new-in-paperback edition provides a comprehensive course in Modern Analysis. The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis, and contain over 120 end of chapter exercises. The final two chapters apply theory to applications in Probability Theory and Partial Differential Equations. - ;This new-in-paperback text is based on lectures given by the author at the advanced undergraduate and graduate levels in Measure Theory, Functional Analysis, Banach Algebras, Spectral Theory (of bounded and unbounded operators), Semigroups of Operators, Probability.  Read more... 1 Measures; 2 Construction of measures; 3 Measure and topology; 4 Continuous linear functionals; 5 Duality; 6 Bounded operators; 7 Banach algebras; 8 Hilbert spaces; 9 Integral representation; 10 Unbounded operators; Application I: Probability; Application II: Distributions; Bibliography; Index