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Lectures on Measure and Integration by Harold Widom is a nonfiction available to read on EtoBox.

What is Lectures on Measure and Integration about?

Chapter I: Measures Definition of measure 3; regular measure 4; outer measure 6; measurable set 8; Hahn extension theorem 10; monotone families of sets 12; completion of measures 14; Borel sets and construc- tion of Lebesgue measure in the real line 15; the Cantor set 16; a non -measurable set 16. Chapter II: Integration Measure spaces and measurable functions 19; definition of the integral for non -negative functions 22; the integral as a measure 23; linearity of the integral 25; monotone convergence theorem 28; Fatou's lemma 30; the integral for real-valued functions 32; the integral for complex -val ued functions 33; dominated convergence theorem 34; bounded convergence theorem 35; Egoroff's theorem 36; convergence in measure 37; L -convergence 39; the Lebesgue p and Riemann integrals 41. Chapter III: The Theorems of Fubini Definition of :r x 'Y 45; simple functions 49; interchange of integration for non -negative functions 51; interchange of integra- tion for Ll functions 51' completion of X x y 52; a theorem on change of variables in integration 54. Chapter IV: Representations of Measures Definition of III I 58; Jordan decomposition theorem 60; Hahn decomposition theorem 62; t

Who reads Lectures on Measure and Integration?

Author

Harold Widom

Publisher

Van Nostrand Reinhold Company

Published

1969

Language

EN

Category

nonfiction