
Instant online reading.
Don't wait for delivery!
Go digital and save!
At a Glance
564 Pages
22.23 x 16.51 x 3.81
Hardcover
RRP $216.99
$195.75
10%OFF
or 4 interest-free payments of $48.94 with
orShips in 15 to 25 business days
Industry Reviews
| Preface | p. v |
| Notations | p. xv |
| Measure Spaces | p. 1 |
| Introduction | p. 1 |
| Measure on a [sigma]-algebra of Sets | p. 3 |
| [sigma]-algebra of Sets | p. 3 |
| Limits of Sequences of Sets | p. 4 |
| Generation of [sigma]-algebras | p. 6 |
| Borel [sigma]-algebras | p. 8 |
| Measure on a [sigma]-algebra | p. 9 |
| Measures of a Sequence of Sets | p. 12 |
| Measurable Space and Measure Space | p. 15 |
| Measurable Mapping | p. 17 |
| Induction of Measure by Measurable Mapping | p. 19 |
| Outer Measures | p. 24 |
| Construction of Measure by Means of Outer Measure | p. 24 |
| Regular Outer Measures | p. 27 |
| Metric Outer Measures | p. 29 |
| Construction of Outer Measures | p. 32 |
| Lebesgue Measure on R | p. 35 |
| Lebesgue Outer Measure on R | p. 35 |
| Some Properties of the Lebesgue Measure Space | p. 39 |
| Existence of Non Lebesgue Measurable Sets | p. 42 |
| Regularity of Lebesgue Outer Measure | p. 44 |
| Lebesgue Inner Measure on R | p. 49 |
| Measurable Functions | p. 61 |
| Measurability of Functions | p. 61 |
| Operations with Measurable Functions | p. 65 |
| Equality Almost Everywhere | p. 68 |
| Sequence of Measurable Functions | p. 69 |
| Continuity and Borel and Lebesgue Measurability of Functions on R | p. 72 |
| Cantor Ternary Set and Cantor-Lebesgue Function | p. 74 |
| Completion of Measure Space | p. 83 |
| Complete Extension and Completion of a Measure Space | p. 83 |
| Completion of the Borel Measure Space to the Lebesgue Measure Space | p. 86 |
| Convergence a.e. and Convergence in measure | p. 88 |
| Convergence a.e. | p. 88 |
| Almost Uniform Convergence | p. 92 |
| Convergence in Measure | p. 94 |
| Cauchy Sequences in Convergence in Measure | p. 100 |
| Approximation by Step Functions and Continuous Functions | p. 102 |
| The Lebesgue Integral | p. 113 |
| Integration of Bounded Functions on Sets of Finite Measures | p. 113 |
| Integration of Simple Functions | p. 113 |
| Integration of Bounded Functions on Sets of Finite Measures | p. 116 |
| Riemann Integrability | p. 124 |
| Integration of Nonnegative Functions | p. 135 |
| Lebesgue Integral of Nonnegative Functions | p. 135 |
| Monotone Convergence Theorem | p. 137 |
| Approximation of the Integral by Truncation | p. 142 |
| Integration of Measurable Functions | p. 147 |
| Lebesgue Integral of Measurable Functions | p. 147 |
| Convergence Theorems | p. 155 |
| Convergence Theorems under Convergence in Measure | p. 158 |
| Approximation of the Integral by Truncation | p. 160 |
| Translation and Linear Transformation of the Lebesgue Integral in R | p. 164 |
| Integration by Image Measure | p. 166 |
| Signed Measures | p. 175 |
| Signed Measure Spaces | p. 175 |
| Decomposition of Signed Measures | p. 179 |
| Integration on a Signed Measure Space | p. 185 |
| Absolute Continuity of a Measure | p. 189 |
| The Radon-Nikodym Derivative | p. 189 |
| Absolute Continuity of a Signed Measure Relative to a Positive Measure | p. 190 |
| Properties of the Radon-Nikodym Derivative | p. 195 |
| Differentiation and Integration | p. 201 |
| Monotone Functions and Functions of Bounded Variation | p. 201 |
| The Derivative | p. 201 |
| Differentiability of Monotone Functions | p. 205 |
| Functions of Bounded Variation | p. 214 |
| Absolutely Continuous Functions | p. 221 |
| Absolute Continuity | p. 221 |
| Banach-Zarecki Criterion for Absolute Continuity | p. 225 |
| Singular Functions | p. 226 |
| Indefinite Integrals | p. 227 |
| Calculation of the Lebesgue Integral by Means of the Derivative | p. 233 |
| Convex Functions | p. 246 |
| Continuity and Differentiability of a Convex Function | p. 246 |
| Monotonicity and Absolute Continuity of a Convex Function | p. 255 |
| Jensen's Inequality | p. 257 |
| The Classical Banach Spaces | p. 261 |
| Normed Linear Spaces | p. 261 |
| Banach Spaces | p. 261 |
| Banach Spaces on R[superscript k] | p. 263 |
| The Space of Continuous Functions C([a, b]) | p. 266 |
| A Criterion for Completeness of a Normed Linear Space | p. 268 |
| Hilbert Spaces | p. 269 |
| The Dual of a Banach Space | p. 271 |
| Semicontinuous Functions | p. 274 |
| The L[superscript p] Spaces | p. 278 |
| The L[superscript p] Spaces for p [set membership] (0, [infinity]) | p. 278 |
| The Linear Spaces L[superscript p] for p [set membership] (1, [infinity]) | p. 281 |
| The L[superscript p] Spaces for p [set membership] (1, [infinity]) | p. 286 |
| The Space L[superscript infinity] | p. 290 |
| The L[superscript p] Spaces for p [set membership] (0, 1) | p. 294 |
| Relation among the L[superscript p] Spaces | p. 298 |
| The Modified L[superscript p] Norms for L[superscript p] Spaces with p [set membership] [1, infinity] | p. 298 |
| Approximation by Continuous Functions | p. 300 |
| L[superscript p] Spaces with p [set membership] (0, 1) | p. 303 |
| The l[superscript p] Spaces | p. 304 |
| Bounded Linear Functionals on the L[superscript p] Spaces | p. 310 |
| Bounded Linear Functionals Arising from Integration | p. 310 |
| Approximation by Simple Functions | p. 313 |
| A Converse of Holder's Inequality | p. 314 |
| Riesz Representation Theorem on the L[superscript p] Spaces | p. 317 |
| Integration on Locally Compact Hausdorff Space | p. 325 |
| Continuous Functions on a Locally Compact Hausdorff Space | p. 325 |
| Borel and Radon Measures | p. 329 |
| Positive Linear Functionals on C[subscript c](X) | p. 331 |
| Approximation by Continuous Functions | p. 338 |
| Extension of Additive Set Functions to Measures | p. 343 |
| Extension of Additive Set Functions on an Algebra | p. 343 |
| Additive Set Function on an Algebra | p. 343 |
| Extension of an Additive Set Function on an Algebra to a Measure | p. 348 |
| Regularity of an Outer Measure Derived from a Countably Additive Set Function on an Algebra | p. 348 |
| Uniqueness of Extension of a Countably Additive Set Function on an Algebra to a Measure | p. 351 |
| Approximation to a [sigma]-algebra Generated by an Algebra | p. 353 |
| Outer Measure Based on a Measure | p. 356 |
| Extension of Additive Set Functions on a Semialgebra | p. 358 |
| Semialebras of Sets | p. 358 |
| Additive Set Function on a Semialgebra | p. 359 |
| Outer Measures Based on Additive Set Functions on a Semialgebra | p. 362 |
| Lebesgue-Stieltjes Measure Spaces | p. 365 |
| Lebesgue-Stieltjes Outer Measures | p. 365 |
| Regularity of the Lebesgue-Stieltjes Outer Measures | p. 368 |
| Absolute Continuity and Singularity of a Lebesgue-Stieltjes Measure | p. 369 |
| Decomposition of an Increasing Function | p. 378 |
| Product Measure Spaces | p. 385 |
| Existence and Uniqueness of Product Measure Spaces | p. 385 |
| Integration on Product Measure Space | p. 389 |
| Completion of Product Measure Space | p. 400 |
| Convolution of Functions | p. 404 |
| Some Related Theorems | p. 411 |
| Measure and Integration on the Euclidean Space | p. 417 |
| Lebesgue Measure Space on the Euclidean Space | p. 417 |
| Lebesgue Outer Measure on the Euclidean Space | p. 417 |
| Regularity Properties of Lebesgue Measure Space on R[superscript n] | p. 422 |
| Approximation by Continuous Functions | p. 424 |
| Lebesgue Measure Space on R[superscript n] as the Completion of a Product Measure Space | p. 427 |
| Translation of the Lebesgue Integral on R[superscript n] | p. 429 |
| Linear Transformation of the Lebesgue Integral on R[superscript n] | p. 430 |
| Differentiation on the Euclidean Space | p. 438 |
| The Lebesgue Differentiation Theorem on R[superscript n] | p. 438 |
| Differentiation of Set Functions with Respect to the Lebesgue Measure | p. 448 |
| Signed Borel Measures on R[superscript n] | p. 448 |
| Differentiation of Borel Measures with Respect to the Lebesgue Measure | p. 450 |
| Differentiation of the Indefinite Integral | p. 454 |
| Density of Lebesgue Measurable Sets Relative to the Lebesgue Measure | p. 455 |
| Change of Variable of Integration on the Euclidean Space | p. 460 |
| Change of Variable of Integration by Differentiable Transformations | p. 460 |
| Spherical Coordinates in R[superscript n] | p. 471 |
| Integration by Image Measure on Spherical Surfaces | p. 478 |
| Hausdorff Measures on the Euclidean Space | p. 485 |
| Hausdorff Measures | p. 485 |
| Hausdorff Measures on R[superscript n] | p. 485 |
| Equivalent Definitions of Hausdorff Measure | p. 489 |
| Regularity of Hausdorff Measure | p. 495 |
| Hausdorff Dimension | p. 498 |
| Transformations of Hausdorff Measures | p. 503 |
| Hausdorff Measure of Transformed Sets | p. 503 |
| 1-dimensional Hausdorff Measure | p. 508 |
| Hausdorff Measure of Jordan Curves | p. 509 |
| Hausdorff Measures of Integral and Fractional Dimensions | p. 514 |
| Hausdorff Measure of Integral Dimension and Lebesgue Measure | p. 514 |
| Calculation of the n-dimensional Hausdorff Measure of a Unit Cube in R[superscript n] | p. 516 |
| Transformation of Hausdorff Measure of Integral Dimension | p. 522 |
| Hausdorff Measure of Fractional Dimension | p. 527 |
| Bibliography | p. 537 |
| Index | p. 539 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9789810239367
ISBN-10: 981023936X
Published: 1st December 1998
Format: Hardcover
Language: English
Number of Pages: 564
Audience: College, Tertiary and University
Publisher: WORLD SCIENTIFIC PUB CO INC
Country of Publication: SG
Dimensions (cm): 22.23 x 16.51 x 3.81
Weight (kg): 0.93
Shipping
| Standard Shipping | Express Shipping | |
|---|---|---|
| Metro postcodes: | $9.99 | $14.95 |
| Regional postcodes: | $9.99 | $14.95 |
| Rural postcodes: | $9.99 | $14.95 |
Orders over $79.00 qualify for free shipping.
How to return your order
At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.
Additional postage charges may be applicable.
Defective items
If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.
For more info please visit our Help Centre.
You Can Find This Book In

Essential Math for Data Science
Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics
Paperback
RRP $125.75
$60.99
OFF























