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Boas R.P. — A Primer of Real Functions
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Название: A Primer of Real FunctionsАвтор: Boas R.P. Аннотация: This is a revised, updated and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic covered sets, metric spaces, continuous functions, and differentiable functions. The greatly expanded fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Fourth EditionГод издания: 1996Количество страниц: 314Добавлена в каталог: 11.04.2008Операции: Положить на полку |
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Continuous functions, ranges of 93 Continuous functions, represented by formulas 82 Continuous functions, separable space 43 Continuous functions, two-to-one 94—95 Continuous functions, uniform continuity 127 Continuous functions, uniform convergence 110—122 Continuous functions, velocity 156 Continuous functions, with connected domains 92 Continuous functions, with continuous inverse 91 Continuous functions, with equal derivatives 164—165 Continuous functions, with infinite derivative 151 Continuous functions, with zero derivative 161—163 Continuous on the right 87 140 Continuum Hypothesis 210 Convergence 52—61 Convergence, Abel’s test 233 Convergence, absolute 209 Convergence, almost uniform 202 Convergence, bounded 111 213 Convergence, dominated 212 Convergence, Fatou’s lemma 213 Convergence, integral test 220 Convergence, mean square 222 Convergence, monotone 214 Convergence, necessary condition 183 Convergence, of derivatives 145—147 171—172 Convergence, of monotonic functions 159 Convergence, of sequences and series 52—56 237—243 Convergence, of sequences of functions 108—111 Convergence, of Taylor series 189—192 Convergence, pointwise 108—109 Convergence, radius of 192 Convergence, uniform 110—122 Convex, curves 102 Convex, functions 175—186 200 Convex, pancakes 102 Convex, strictly 180 Cooke, Roger L. 200 coordinates 17 Copson, Edward Thomas 52 61 Corominas, Ernest 72 Countable sets 8—20 Countable sets, algebraic numbers 11 Countable sets, dense 42 Countable sets, disjoint intervals 30 Countable sets, integers 9 Countable sets, jumps of monotonic functions 159 Countable sets, lattice points 10 Countable sets, measure zero 74 Countable sets, polynomials 11 43 Countable sets, proper maxima 142 Countable sets, rational numbers 11 Countable sets, subsets 10 Countable sets, union of 10 11 Countably additive 198 Countably infinite 9 Counting 8 Covering 2 48—52 73 172 Cox, Raymond H. 21 Cross section 166 Cross-shaped sets 134 Cup of coffee 102 Curve, area under 195 Curve, continuous 114—117 Curve, convex 102 179 Curve, space-filling 114 Cusp 71 Darboux functions 90 Darboux, Gaston 89 Darst, Richard B. 158 193 De La Vallee Poussin, Charles Jean 126 Decimals 12—15 17—20 40—42 84 237 Decomposition of a closed interval 72 Decreasing function 158 Denjoy, Arnaud 72 Dense sets 38—44 Density, point of 172 Derivates 139—155 Derivates, at a maximum 142 Derivates, bounds of 150 Derivates, continuous 151 Derivates, infinite 152 Derivates, mean—value theorem 149 Derivates, nonnegative 150 Derivates, of arbitrary function 155 Derivates, of continuous function 149—151 Derivates, of discontinuous function 150 152 Derivates, of sums 140 Derivates, zero 154 derivatives 66 139—155 Derivatives, at maximum 142 Derivatives, behave worse 148 Derivatives, bounded 70 Derivatives, cannot jump 151 Derivatives, chain rule 141 Derivatives, continuous 118 Derivatives, discontinuous 151 Derivatives, finite 154 215 Derivatives, Fubini’s theorem 171 Derivatives, infinite 140 151 174 Derivatives, integrals of 215—216 Derivatives, integration by parts 228 Derivatives, intermediate values 100 143 Derivatives, level sets 152 Derivatives, limits of 151 187 Derivatives, nonexistent 70—72 153 154 Derivatives, nonnegative 149 191 Derivatives, not everywhere infinite 151 Derivatives, not integrable 119 215 Derivatives, of composite function 141 Derivatives, of convex functions 177 Derivatives, of delta function 228 Derivatives, of fixed sign 191 Derivatives, of infinite order 118 Derivatives, of integrals 214—215 Derivatives, of jump function 161 Derivatives, of monotonic functions 165—170 Derivatives, of periodic function 143 Derivatives, of sequence 119 145—147 Derivatives, of series 171—172 Derivatives, positive 141 Derivatives, product of 155 Derivatives, range of 143—145 Derivatives, right-hand 140 Derivatives, zero 67 142 160—164 204 Desert, Sahara 46 DeTemple, Duane W. 244 Determinant 135 Devlin, Keith 21 Diameter 50 59—61 Diamond, Harvey 75 Diaz, Joaquin Basilio 103 156 157 Dieudonne, Jean Alexandre 156 Difference quotient 68 143—145 150 178—179 Differences 133 199 Differentiation see “Derivatives” Dilation 199 Dini derivates see “Derivatives” Dini, Ulisse 155 Dini’s theorem 112 122 Disconnected, totally 42 discontinuous functions 87 112 226 Discontinuous functions, examples 84 85 108 125 133 150 151 159 Discontinuous functions, properties 89 93 114 123 125 151 153 175 Discontinuous functions, with infinite derivative 140 dishes 2 Disjoint 3 Disk 11 25 Dispersion point 33 Distance 21—25 Distance, as continuous function 88 Distance, between sets 61 Distance, from point to set 88 173 Distributions 228 diverge 54 Divergent Taylor series 189—190 Divide et impera 264 Domain 77 Dominate 211 Dominated convergence 212 Dot product 221 Drobot, Vladimir 156 Duality 75 234 Dutch 225 Egoroff’s theorem 202 205 212 Egorov’s theorem see “Egoroff’s theorem” Element 1 2 Elements of Euclid 200 Empty set 2 Empty set, bounds of 8 Empty set, countable 9 Empty set, is open and closed 28 Engine 202 English words 4 Ensemble 2 Equations defining functions 78 82 Equilateral triangle 255 Equivalence class 210 217 Equivalence theorem 21 Erdos, Paul 157 175 Ergodic theorem 202 Erratic clock 262 Error 108 151 238 243 Essential supremum 218 Euclid 200 Euler — Maclaurin formula 239—243 Euler’s constant 240 Everywhere dense 38 exception 80 141 155 166 Existence proof 14 72 Expansion, formal 221 Expectation 224 Exponential function 118 120 190 191 Extremal problems 182 Factor, prime 82 Fallacious proof 15 141 Fast, Henryk 90 Fatou’s Lemma 213 223 276 Fence 46 Field 79 Filipczak, F.M. 157 Finite, sequence 53 Finite, set 9 16 Finite, subsets 12 Fink, Arlington M. 186 First category 64 73 First category, analytic functions are set of 193 First category, but not measure zero 74 First category, countable set need not be 64 First category, differentiable functions form set of 70 First category, duality with measure zero 75 First category, of level sets 152 First category, points of discontinuity form set of 125 153 Fischer, Ernst 222 224 Fixed fraction 75 169 172 Fixed-point theorem 100 102 Flett, Thomas Muirhead 103 156 Flowing water lemma 166 Folland, Gerald B. 229 Formal expansion 221 formulas 81—82 Fort, Marion Kirkland, Jr. 157 Fort’s theorem 153—154 157 Fourier series 221 225 231 Fourteenth century 256 Fox, William C. 52 Frank, Alan 20 Freilich, Gerald 174 French language 2 123 French mathematician 229 French, Robert M. 200 Frong 4 Frontier point 27 Frullani integrals 139 Fubini’s Theorem 164 171 173 175 215 Functional 233—236 Functional analysis 207 Functions 77—83 Functions, absolutely continuous 204—205 Functions, abstract definition 77—79 Functions, analytic 47 69 189—192 Functions, approximation of 47 Functions, arbitrary 84—85 87 154—155 Functions, Baire classes 125 201—202 Functions, bounded 25 44—46 48 111 209 Functions, cardinality of set of 17 Functions, constant 78 Functions, continuous 83—102 123—132 Functions, convex 175—186 Functions, Darboux 84 Functions, defined by equations 78 Functions, defined by formulas 81—82 Functions, delta 228 Functions, differentiable 139—155 Functions, discontinuous 84 86 87 89 93 112 114 123—126 133 140 150 153 175 Functions, distance 22 Functions, generalized 140 228 Functions, greatest integer 158 227 238 277 Functions, identity 81 Functions, infinitely differentiate 118 120 186—192 Functions, integrate 202 206 208—210 Functions, inverse 91 Functions, jump 160 Functions, linear 132—138 Functions, measurable 201—205 Functions, monotonic 113 141 155 158—174 Functions, multiple—valued 77 Functions, nondifferentiable 70—72 153 Functions, notations for 80—81 Functions, of a real variable 79 Functions, one-to-one 91 94 Functions, orthogonal 221—224 Functions, oscillating 69—70 Functions, oscillating differentiate 70 Functions, periodic 97—98 143 238 240 Functions, polygonal 127 128 Functions, restriction of 86—87 Functions, ruler 85 154 158 218 Functions, saw-tooth 70 Functions, sequences of 108—111 Functions, sine 182 Functions, singular 161—164 174 204 Functions, spaces of 24—25 Functions, step 127 128 214 226 276 Functions, strictly monotonic 94 Functions, tangent 247 270 Functions, two-to-one 94 Functions, univalent 91 Functions, wiggly 70 Functions, with equal derivatives 154 164—165 Fundamental theorem of algebra 59 Fundamental theorem, of calculus 195 214 Galilei, Galileo 156 Game 52 Garg, Krishna Murari 157 Gelbaum, Bernard R. 72 Gelles, Gregory 75 Generalized, Cantor set 74—75 206 Generalized, function 140 228 Geometric mean 181—183
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