Yeh J. Problems and proofs in real analysis: theory of measure and integration. - Singapore: Word scientific, 2014. - viii, 491 p. - ISBN 978-981-4578-50-9 Шифр: (И/В16-Y39) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ..................................................... viii §1 Measure on а ст-algebra of Sets ............................ 1 §2 Outer Measures ............................................ 43 §3 Lebesgue Measure on R ..................................... 46 §4 Measurable Functions ...................................... 78 §5 Completion of Measure Space .............................. 104 §6 Convergence a.e. and Convergence in Measure .............. 107 §7 Integration of Bounded Functions on Sets of Finite Measure .................................................. 132 §8 Integration of Nonnegative Functions ..................... 160 §9 Integration of Measurable Functions ...................... 192 §10 Signed Measures .......................................... 266 §11 Absolute Continuity of a Measure ......................... 277 §12 Monotone Functions and Functions of Bounded Variation .... 290 §13 Absolutely Continuous Functions .......................... 314 §16 The Lp Spaces ............................................ 353 §17 Relation among the Lp Spaces ............................. 386 §18 Bounded Linear Functionals on the Lp Spaces .............. 424 §22 Lebesgue-Stieltjes Measure Spaces ........................ 431 §23 Product Measure Spaces ................................... 443 §24 Lebesgue Measure Space on the Euclidean Space ............ 466 §25 Differentiation on the Euclidean Space ................... 473