Sold Out
Book Categories |
Preface | ||
Ch. I | Review | 1 |
I.1 | Introduction | 1 |
I.2 | Notation | 3 |
I.3 | The Theorem of Stone-Weierstrass | 8 |
I.4 | The Riemann Integral | 17 |
I.5 | An Integrability Criterion | 21 |
I.6 | The Permanence Properties | 23 |
I.7 | Seminorms | 28 |
Ch. II | Extension of the Integral | 31 |
II.1 | [Sigma]-additivity | 33 |
II.2 | Elementary Integrals | 35 |
II.3 | The Daniell Mean | 42 |
II.4 | Negligible Functions and Sets | 48 |
II.5 | Integrable Functions | 52 |
II.6 | Extending the Integral | 58 |
II.7 | Integrable Sets | 61 |
II.8 | Example of a Non-Integrable Function | 66 |
Ch. III | Measurability | 69 |
III.1 | Littlewood's Principles | 70 |
III.2 | The Permanence Properties | 73 |
III.3 | The Integrability Criterion | 75 |
III.4 | Measurable Sets | 81 |
III.5 | Baire and Borel Functions | 85 |
III.6 | Further Properties of Daniell's Mean | 92 |
III.7 | The Procedures of Lebesgue and Carathedory | 95 |
Ch. IV | The Classical Banach Spaces | 101 |
IV.1 | The p-norms | 102 |
IV.2 | The [actual symbol not reproducible]-spaces | 105 |
IV.3 | The L[superscript p] spaces | 108 |
IV.4 | Linear Functionals | 112 |
IV.5 | The Dual of L[superscript p] | 118 |
IV.6 | The Hilbert space L[superscript 2] | 122 |
Ch. V | Operations on Measures | 125 |
V.1 | Products of Elementary Integrals | 125 |
V.2 | The Theorems of Fubini and Tonelli | 130 |
V.3 | An Application: Convolution | 133 |
V.4 | An Application: Marcinkiewicz Interpolation | 134 |
V.5 | Signed Measures | 137 |
V.6 | The Space of Measures | 144 |
V.7 | Measures with Densitites | 151 |
V.8 | The Radon-Nikodym Theorem | 154 |
V.9 | An Application: Conditional Expectation | 155 |
V.10 | Differentiation | 157 |
App. A: Answers to Selected Problems | 165 | |
References | 180 | |
Index of Notations | 181 | |
Index | 184 |
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionIntegration - A Functional Approach
X
This Item is in Your InventoryIntegration - A Functional Approach
X
You must be logged in to review the productsX
X
X
Add Integration - A Functional Approach, , Integration - A Functional Approach to the inventory that you are selling on WonderClubX
X
Add Integration - A Functional Approach, , Integration - A Functional Approach to your collection on WonderClub |