| Preface |
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| Conventions and notation |
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1 | (6) |
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1.1 Areas of planar regions |
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1 | (3) |
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1.2 Center of mass and moments |
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4 | (1) |
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5 | (2) |
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2 Functions of bounded variation |
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7 | (50) |
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2.1 Definition and basic properties |
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7 | (11) |
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2.2 Space of functions of bounded variation |
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18 | (2) |
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2.3 Bounded variation and continuity |
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20 | (4) |
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2.4 Derivatives of bounded variation functions |
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24 | (2) |
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26 | (8) |
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2.6 Decomposition into continuous and jump parts |
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34 | (5) |
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2.7 Pointwise convergence |
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39 | (4) |
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2.8 Variation on elementary sets |
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43 | (14) |
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3 Absolutely continuous functions |
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57 | (16) |
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3.1 Definition and basic properties |
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57 | (4) |
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3.2 Absolutely continuous functions and the Lebesgue integral |
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61 | (5) |
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3.3 Lebesgue decomposition of functions of bounded variation |
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66 | (7) |
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73 | (16) |
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4.1 Definition and basic properties |
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73 | (6) |
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4.2 Space of regulated functions and its subspaces |
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79 | (3) |
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4.3 Relatively compact subsets of G([ a, b]) |
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82 | (7) |
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5 Riemann-Stieltjes integral |
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89 | (50) |
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5.1 Definition and basic properties |
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89 | (14) |
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103 | (6) |
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5.3 Absolute integrability |
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109 | (7) |
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116 | (3) |
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119 | (2) |
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5.6 Existence of the integral |
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121 | (3) |
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124 | (5) |
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5.8 Consequences of Riemann-Stieltjes integrability |
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129 | (4) |
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133 | (2) |
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5.10 Other integrals of Stieltjes type |
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135 | (4) |
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6 Kurzweil-Stieltjes integral |
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139 | (106) |
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139 | (1) |
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6.2 Definition and basic properties |
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140 | (10) |
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6.3 Existence of the integral |
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150 | (16) |
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166 | (3) |
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6.5 The indefinite integral |
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169 | (6) |
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175 | (4) |
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6.7 Absolute integrability |
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179 | (4) |
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183 | (21) |
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6.9 Integration over elementary sets |
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204 | (7) |
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6.10 Integrals of vector, matrix and complex functions |
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211 | (3) |
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6.11 Relation to the Perron-Stieltjes integral |
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214 | (5) |
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6.12 Relation to the Lebesgue-Stieltjes integral |
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219 | (13) |
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6.13 Relation to other Stieltjes-type integrals |
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232 | (13) |
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7 Generalized linear differential equations |
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245 | (46) |
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245 | (2) |
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7.2 Differential equations with impulses |
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247 | (3) |
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250 | (1) |
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7.4 Existence and uniqueness of solutions |
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251 | (6) |
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7.5 A priori estimates of solutions |
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257 | (7) |
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7.6 Continuous dependence of solutions on parameters |
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264 | (9) |
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273 | (7) |
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7.8 Variation of constants formula |
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280 | (11) |
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8 Miscellaneous additional topics |
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291 | (72) |
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8.1 Functionals on the space of continuous functions |
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291 | (8) |
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8.2 Functionals on spaces of regulated functions |
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299 | (7) |
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8.3 Adjoint classes of Kurzweil-Stieltjes integrable functions |
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306 | (9) |
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315 | (5) |
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8.5 Generalized elementary functions |
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320 | (18) |
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8.6 Integration on time scales |
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338 | (10) |
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8.7 Dynamic equations on time scales |
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348 | (15) |
| Bibliography |
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363 | (14) |
| Subject index |
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377 | (4) |
| Symbol index |
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