| Preface | p. V |
| Introduction and Overview | p. 1 |
| How to Define f dg? | p. 2 |
| Some Integral and Differential Equations | p. 7 |
| Basic Assumptions | p. 9 |
| Notation and Elementary Notions | p. 10 |
| Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals | p. 17 |
| Regulated and Interval Functions | p. 17 |
| Riemann-Stieltjes Integrals | p. 24 |
| The Refinement Young-Stieltjes and Kolmogorov Integrals | p. 29 |
| Relations between RS, RRS, and RYS Integrals | p. 46 |
| The Central Young Integral | p. 51 |
| The Henstock-Kurzweil Integral | p. 56 |
| Ward-Perron-Stieltjes and Henstock-Kurzweil Integrals | p. 62 |
| Properties of Integrals | p. 71 |
| Relations between Integrals | p. 87 |
| Banach-Valued Contour Integrals and Cauchy Formulas | p. 90 |
| Notes | p. 98 |
| -variation and p-variation; Inequalities for Integrals | p. 103 |
| -variation | p. 103 |
| Interval Functions, -variation, and p-variation | p. 116 |
| Elementary Properties | p. 127 |
| A Necessary and Sufficient Condition for Integral Duality | p. 148 |
| Sufficient Conditions for Integrability | p. 168 |
| Love-Young Inequalities | p. 173 |
| Existence of Extended Riemann-Stieltjes Integrals | p. 191 |
| Convolution and Related Integral Transforms | p. 196 |
| Notes | p. 211 |
| Banach Algebras | p. 215 |
| Ideals and Normed Algebras | p. 216 |
| The Spectral Radius | p. 219 |
| Characters | p. 222 |
| Holomorphic Functions of Banach Algebra Elements | p. 225 |
| Complexification of Real Banach Algebras | p. 231 |
| A Substitution Rule for the Kolmogorov Integral | p. 233 |
| Notes | p. 234 |
| Derivatives and Analyticity in Normed Spaces | p. 237 |
| Polynomials and Power Series | p. 239 |
| Higher Order Derivatives and Taylor Series | p. 251 |
| Taylor's Formulas | p. 264 |
| Tensor Products of Banach Spaces | p. 269 |
| Notes | p. 270 |
| Nemytskii Operators on Some Function Spaces | p. 273 |
| Overview | p. 273 |
| Remainders in Differentiability | p. 274 |
| Higher Order Differentiability and Analyticity | p. 276 |
| Autonomous Nemytskii Operators on Wp Spaces | p. 293 |
| Nemytskii Operators on Wp Spaces | p. 300 |
| Higher Order Differentiability and Analyticity on Wp Spaces | p. 323 |
| Notes | p. 333 |
| Nemytskii Operators on Lp Spaces | p. 335 |
| Acting, Boundedness, and Continuity Conditions | p. 335 |
| Hölder Properties | p. 347 |
| Differentiability | p. 354 |
| Higher Order Differentiability and Finite Taylor Series | p. 368 |
| Examples where NF Is Differentiable and F Is Not | p. 378 |
| Notes | p. 390 |
| Two-Function Composition | p. 393 |
| Overview; General Remarks | p. 393 |
| Differentiability of Two-Function Composition in General | p. 394 |
| Measure Space Domains | p. 397 |
| Spaces with Norms Stronger than Supremum Norms | p. 401 |
| Two-Function Composition on Wp Spaces | p. 404 |
| Notes | p. 405 |
| Product Integration | p. 407 |
| Multiplicative Interval Functions and -Variation | p. 408 |
| Product Integrals for Real-Valued Interval Functions | p. 415 |
| Nonexistence for p > 2 | p. 424 |
| Inequalities for Finite Products | p. 425 |
| The Product Integral | p. 430 |
| The Strict Product Integral | p. 432 |
| Commutative Banach Algebras | p. 438 |
| Integrals with Two Integrands | p. 442 |
| Duhamel's Formula | p. 451 |
| Smoothness of the Product Integral Operator | p. 457 |
| Linear Integral Equations | p. 474 |
| Integral Equations for Banach-Space-Valued Functions | p. 494 |
| Notes | p. 499 |
| Nonlinear Differential and Integral Equations | p. 505 |
| Classical Picard Iteration | p. 505 |
| Picard's Method in p-Variation Norm, 1 < p < 2 | p. 506 |
| Existence and Uniqueness | p. 513 |
| Boundedness and Convergence of Picard Iterates | p. 527 |
| Continuity of the Solution Mappings | p. 536 |
| Notes | p. 549 |
| Fourier Series | p. 551 |
| On the Order of Decrease of Fourier Coefficients | p. 551 |
| Uniform Convergence | p. 554 |
| Notes | p. 568 |
| Stochastic Processes and -Variation | p. 571 |
| Processes with Regulated Sample Functions | p. 571 |
| Brownian Motion | p. 575 |
| Martingales | p. 576 |
| Gaussian Stochastic Processes | p. 579 |
| Markov Processes | p. 600 |
| Lévy Processes | p. 611 |
| Empirical Processes | p. 615 |
| Differentiability of Operators on Processes | p. 628 |
| Integration | p. 629 |
| Notes | p. 640 |
| Appendix Nonatomic Measure Spaces | p. 645 |
| References | p. 649 |
| Subject Index | p. 661 |
| Author Index | p. 665 |
| Index of Notation | p. 669 |
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