| Preface | p. v |
| The one-dimensional Henstock-Kurzweil integral | p. 1 |
| Introduction and Cousin's Lemma | p. 1 |
| Definition of the Henstock-Kurzweil integral | p. 4 |
| Simple properties | p. 8 |
| Saks-Henstock Lemma | p. 4 |
| Notes and Remarks | p. 20 |
| The multiple Henstock-Kurzweil integral | p. 1 |
| Preliminaries | p. 21 |
| The Henstock-Kurzweil integral | p. 25 |
| Simple properties | p. 28 |
| Saks-Henstock Lemma | p. 35 |
| Fubini's Theorem | p. 43 |
| Notes and Remarks | p. 51 |
| Lebesgue integrable functions | p. 3 |
| Introduction | p. 53 |
| Some convergence theorems for Lebesgue integrals | p. 56 |
| m-measurable sets | p. 63 |
| A characterization of m-measurable sets | p. 70 |
| m-measurable functions | p. 73 |
| Vitali Covering Theorem | p. 79 |
| Further properties of Lebesgue integrable functions | p. 82 |
| The LP spaces | p. 84 |
| Lebesgue's criterion for Riemann integrability | p. 88 |
| Some characterizations of Lebesgue integrable functions | p. 91 |
| Some results concerning one-dimensional Lebesgue integral | p. 101 |
| Notes and Remarks | p. 104 |
| Further properties of Henstock-Kurzweil integrable functions | p. 107 |
| A necessary condition for Henstock-Kurzweil | p. 107 |
| A result of Kurzweil and Jarník | p. 108 |
| Some necessary and sufficient conditions for Henstock-Kurzweil integrability | p. 117 |
| Harnack extension for one-dimensional Henstock-Kurzweil integrals | p. 119 |
| Other results concerning one-dimensional Henstock-Kurzweil integral | p. 128 |
| Notes and Remarks | p. 132 |
| The Henstock variational measure | p. 35 |
| Lebesgue outer measure | p. 135 |
| Basic properties of the Henstock variational measure | p. 138 |
| Another characterization of Lebesgue integrabl | p. 145 |
| A result of Kurzweil and Jarnik revisited | p. 148 |
| A measure-theoretic characterization of the Henstock-Kurzweil integral | p. 156 |
| Product variational measures | p. 164 |
| Notes and Remarks | p. 168 |
| Multipliers for the Henstock-Kurzweil integral | p. 69 |
| One-dimensional integration by parts | p. 169 |
| On functions of bounded variation in the sense of Vitali | p. 175 |
| The m-dimensional Riemann-Stieltjes integral | p. 180 |
| A multiple integration by parts for the Henstock-Kurzweil integral | p. 184 |
| Kurzweil's multiple integration by parts formula for the Henstock-il integral | p. 187 |
| Riesz Representation Theorems | p. 194 |
| Characterization of multipliers for the Henstock-Kurzweil integral | p. 198 |
| A Banach-Steinhaus Theorem for the space of Henstock-Kurzweil integrable functions | p. 200 |
| Notes and Remarks | p. 202 |
| Some selected topics in trigonometric series | p. 205 |
| A generalized Dirichlet test | p. 205 |
| Fourier series | p. 210 |
| Some examples of Fourier series | p. 213 |
| Some Lebesgue integrability theorems for trigonometric series | p. 218 |
| Boas' results | p. 226 |
| On a result of Hardy and Littlewood concerning Fourier series | p. 229 |
| Notes and Remarks | p. 232 |
| Some applications of the Henstock-Kurzweil integral to double trigonometric serie | p. 233 |
| Regularly convergent double series | p. 233 |
| Double Fourier series | p. 240 |
| Some examples of double Fourier series | p. 246 |
| A Lebesgue integrability theorem for double cosine | p. 250 |
| A Lebesgue integrability theorem for double sine series | p. 257 |
| A convergence theorem for Henstock-Kurzweil integrals | p. 64 |
| Applications to double Fourier series | p. 270 |
| Another convergence theorem for Henstock-Kurzweil integrals | p. 274 |
| A two-dimensional analogue of Boas' theorem | p. 278 |
| A convergence theorem for double sine series | p. 287 |
| Some open problems | p. 290 |
| Notes and Remarks | p. 294 |
| Bibliography | p. 295 |
| Points, intervals and partitions | p. 305 |
| Functions, integrals and function spaces | p. 307 |
| Measures and outer measures | p. 309 |
| Miscellaneous | p. 311 |
| General index | p. 313 |
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