Selected Problems in Real AnalysisAmerican Mathematical Soc. - Всего страниц: 370 This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore. |
Содержание
| 3 | |
Sequences | 17 |
Functions | 25 |
Series | 35 |
Integrals | 47 |
Asymptotics | 53 |
Functions Continuation | 67 |
Lebesgue Measure and the Lebesgue Integral | 87 |
Introduction | 143 |
Sequences | 157 |
Functions | 167 |
Series | 179 |
Integrals | 201 |
Asymptotics | 213 |
Functions Continuation | 231 |
Lebesgue Measure and the Lebesgue Integral | 263 |
Sequences of Measurable Functions | 109 |
Iterates of Transformations of an Interval | 125 |
Solutions | 141 |
Sequences of Measurable Functions | 301 |
Iterates of Transformations of an Interval | 317 |
Часто встречающиеся слова и выражения
a₁ a₂ Abel transformation arbitrary assertion assumed b₁ bounded c₁ Cantor function Cantor set change of variable closed intervals compute Consider the function Consider the set continuous function converges convex countable defined denoted diverges equality equation equivalent ergodic estimate exists Find the asymptotics finite fixed point follows formula Fourier function ƒ ƒ and g graph hence Hölder inequality homeomorphism implies induction integral invariant Jensen's inequality Lebesgue measure Let f Let f(x limit mapping monotone nonnegative open intervals P₁ partial sums polygonal curve polynomial positive number preceding problem Prove that ƒ real numbers result of problem satisfying the condition sequence solution is analogous solution of problem subset suffices Suppose that ƒ theorem topologically conjugate values Verify x₁ Xn+1 zero