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| Hobson E.W. — Theory of Functions of a Real Variable and the Theory of Fourier's Series V1 |
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| Предметный указатель |
Adherence 126
Aggregate, closed 207
Aggregate, comparable and incomparable 192 253
Aggregate, definition of 189 236
Aggregate, definition of finite 3
Aggregate, dense in itself 207
Aggregate, elements of 1
Aggregate, equivalent 9 239
Aggregate, everywhere dense 207
Aggregate, finite, similar 4 203 240
Aggregate, general notion of 1
Aggregate, general theory of 235
Aggregate, limiting elements of 206
Aggregate, normally ordered 211
Aggregate, of order-types  208
Aggregate, ordinal number of 4 216
Aggregate, parts of 191
Aggregate, perfect 50 207
Aggregate, power of 83
Aggregate, rank of elements in 6
Aggregate, segment of normally ordered 213
Aggregate, simply ordered 203 240
Aggregate, straight line as 57
Aggregate, structure of simply ordered 205
Aleph-numbers 194
Aleph-numbers, general theory of 223 244
Ampere 332
Archimedean system 41
Archimedes 41
Archimedes, axiom of 55
Arithmetization 14
Arithmetization Kronecker's scheme of 22
Arzela 177 322 325 484
Ascoli 53 71 433
Baire 74 115 129 152 249 290 293 295 421 422 423
Baker, H.F. 107
Beman 10
Bendixson 58 112 122
Bernstein 196 200 203 211 227 230 231 233 237 245 252
Bettazzi 52 302
Biermann 22
BLISS 607
Bolza 151 409
Bolzano 60 188
Bonnet 565
Borel 74 106 107 136 154 170 172 177 196 199 242 248 249 273 527
Broden 119 133 260 262 364 366 367 378
Bromwich 332
Brouwer 139 152
Burali — Forti 243 245 247
Cantor, G. 10 22 27 29 30 31 39 41 48 50 51 57 58 71 73 74 78 79 80 81 82 84 88 90 91 94 95 97 116 118 123 154 156 181 188 189 190 195 198 211 223 224 226 228 229 235 237 238 239 240 243 251 252 254 345 424
Cantor, M. 20 36
Caratheodory 154
Cardinal numbers, addition and multiplication of 192
Cardinal numbers, as exponents 193
Cardinal numbers, definition of 9 190 239
Cardinal numbers, division of 200
Cardinal numbers, exceeded by other cardinal numbers 198
Cardinal numbers, of aggregate of continuous functions 272
Cardinal numbers, of continuum 228 232
Cardinal numbers, of second class of ordinals 221
Cardinal numbers, relative order of 191
Cardinal numbers, smallest transfinite 194
Categories, first and second 129
Cathcart 396
Cauchy 107 266 268 271 431 433 464
Coherence 126
Congruency, axiom of 54
Connexity of aggregate of real numbers 50
Content, of sets of points 154 162
Continuity, of functions 266
Continuity, of functions, absolute 276
Continuity, of functions, approximate 295
Continuity, of functions, in the extended sense 277
Continuity, of functions, uniform 274
Continuous functions 267
Continuous functions, construction of 364
Continuous functions, defined at points of set 272
Continuous functions, defined for a continuous interval 270
Continuous functions, in an open interval 288
Continuous functions, oscillating 351 362
Continuous functions, two definitions not equivalent 271
Continuum, arithmetic 85
Continuum, cardinal number of 228 232
Continuum, given by intuition 53
Continuum, of p-dimensions 84
Continuum, of real numbers 50
Continuum, order-type of 208
Continuum, straight line as 54
Convergence, general principle of 37
Correspondence, general notion of 2
Couturat 10
Curves filling space 423 et seq.
Dantscher 417
Darboux 433
Dedekind 10 21 22 30 31 32 39 41 191 245
Denjoy 131 132 150 182 295 376 377 629 636 653 656 661
Derivatives, bounded 352
Derivatives, general properties of 368
Derivatives, of functions 330
Derivatives, of sets of points 71 78 95
Derivatives, progressive and regressive 332
Derivatives, properties of 342 356 538
Derivatives, upper and lower 333
Differential coefficients 331 334
Differential coefficients, higher partial 397
Differential coefficients, partial 392
Differential coefficients, successive 345
Dini 285 299 334 343 363 367 407 416 439 440
Dirichlet 259 260 280 303 431
Discontinuity, classification 284
Discontinuity, infinite 265
Discontinuity, of first and second kinds 284
Discontinuity, of functions 283
Discontinuity, ordinary 286
Discontinuous functions, classification of 296
Discontinuous functions, definition of, by extension 304
Discontinuous functions, point-wise 297 299
Dixon, A.C. 585
Du Bois Reymond 10 37 38 53 58 71 72 74 112 333 359 367 444 463 466 480 487 565 566
Enumerable aggregate, algebraical numbers 80
Enumerable aggregate, definition 78
Enumerable aggregate, isolated sets 99
Enumerable aggregate, rational numbers 80
Equivalence theorem 196
Euclid 19 53
Euler 48 258
Extent, exterior and interior 183
Faber 80
Fluctuation, of function 264
Fluctuation, of function, inner 264
FOURIER 58 258
fractional numbers 13
Frege 1 10
Frontier of set of points 75 141
Fubini 561 577
Functional image 258
Functional limits, aggregate of 281
Functional limits, approximately continuous 295
Functional limits, bounded 263
Functional limits, classification of discontinuous 296
Functional limits, construction of continuous 364
Functional limits, continuity of 266
Functional limits, continuity of unbounded 276
Functional limits, defined implicitly 407
Functional limits, derivatives of 330
Functional limits, differential coefficients of 334
Functional limits, double and repeated limits of 381
Functional limits, existence and equality of repeated limits of 388
Functional limits, homonomically and heteronomically defined 260
| Functional limits, limits of monotone, of two variables 390
Functional limits, limits of, at a point 278
Functional limits, linear in each interval of a set 461
Functional limits, maxima and minima and lines of invariability 326
Functional limits, maxima and minima of, of two variables 416
Functional limits, maximum and minimum, at a point 283
Functional limits, measurable 371 517
Functional limits, monotone 301
Functional limits, most nearly continuous 306
Functional limits, of a variable aggregate 262
Functional limits, of bounded total fluctuation 311
Functional limits, of bounded variation 307 322
Functional limits, of two variables 380
Functional limits, ordinary 367
Functional limits, oscillating continuous 351
Functional limits, point-wise discontinuous 299
Functional limits, properties of derivatives of continuous 356
Functional limits, quasi-monotone 325
Functional limits, semi-continuous 290
Functional limits, successive differential coefficients of 345
Functional limits, symmetry of 287
Functional limits, unbounded 264
Functional limits, upper and lower boundaries and limits of 263
Functional limits, upper boundary of, in an interval 264
Functional limits, with bounded derivatives 352
Functional limits, with lines of invariability 344
Functional limits, with one derivative assigned 363
Functional relation 257
Functions, Dirichlet's definition 259
Generation, Cantor's principle of 90
Genocchi 381
Goursat 107
Graphs, functions defined by 367
Grave 345
hadamard 249
Hahn 306 307 455 527 547 598 609 613
Hamilton, W.R. 11
hankel 21 154 156 297 299 303 566
Hardy, G.H. 228 233 250 324 462 498 499
Harnack 58 112 154 156 163 184 300 303 396 431 484 599
Hartog 254
Hausdorff 152 233 237
Hedrick 416
Heine 10 22 30 31 107 266 268 275
Heine — Borel theorem 102
Hellinger 609
Helmholtz 2 10 11
hermite 81
Hessenberg 237
hilbert 38 237 245 427 429
Hildebrandt 527 606 607 615
Hobson 87 139 151 399 409 416 536 566 577 578 613 627
Holder 52 54 566
Huntington 210 237
Husserl 10
Incrementary ratios 354
Incrementary ratios, boundaries of 359
Indeterminate forms, evaluation of 337
Infinitesimals, non-existence of 41
Infinitesimals, Veronese's theory of 56
Integers, sets of sequences of 152
Integrable functions, null-functions 451
Integrable functions, particular cases of 439
Integral calculus, fundamental theorem of 431 452 548 636
Integral numbers, operations on 11
Integral, approximate representation of, as a Riemann sum 585
Integral, Cauchy's definition of improper 464
Integral, change of independent variable in a Lebesgue 592
Integral, change of variable in a single Riemann 476
Integral, conditions of existence of 436
Integral, Denjoy 629
Integral, Denjoy — Khintehine — Young 655
Integral, double, over an infinite domain 495
Integral, equivalent Lebesgue 532
Integral, generalized indefinite 416
Integral, Harnack — Lebesgue 616
Integral, Harnack's definition of an 599
Integral, Hellinger's 609
Integral, improper double 488
Integral, indefinite 540
Integral, indefinite, of a function of two variables 560
Integral, Lebesgue — Stieltjes 605
Integral, Lebesgue, as function of a set of points 530
Integral, lebesgue, as measure of a set of points 528
Integral, lebesgue, of a measurable function 519
Integral, lebesgue, over an unbounded field 589
Integral, non-absolutely convergent 616
Integral, other definitions of an 526
Integral, properties of definite Riemann 442
Integral, properties of Lebesgue 533
Integral, properties of the Denjoy 647
Integral, repeated Lebesgue 573
Integral, repeated Riemann 479
Integral, Riemann 432
Integral, Riemann — Stieltjes 506
Integral, Riemann, of functions of two or more variables 446
Integral, Riemann, over unbounded interval 468
Integral, the Riemann, as a Lebesgue integral 529
Integral, total variation of an indefinite 557
Integral, transformation of double 499
Integral, upper and lower Riemann 433
Integral, upper and lower Riemann — Stieltjes 509
Integral, upper and lower semi 547
Integral, Young 656
Integration, double, by parts 461 563
Integration, geometrical interpretation of 440
Intervals, Lebesgue chain of 109
Intervals, open and closed 51
Intervals, sets of 96
Irrational numbers 1
Irrational numbers Cantor's theory of 27
Irrational numbers Dedekind's theory of 23
Jacob 21
JORDAN 73 141 152 183 307 316 416 433 446 484 488 599 624
Jourdain 200 212 224 237 245 252
Khintchine 653
Konig 87 237 353
Kopcke 364 367
Korselt 196
Kowalewski 566
Krause 324
kronecker 22 566
Kustermann 325
Lambert 48
Lebesgue 109 154 159 178—182 249 271 316 317 363 376 427 431 436 478 517 527 534 541 549 559 570 571 577 582 586 588 592 607 624
legendre 47 48
Leibnitz 1
Levi, B. 252 536 549
Limits, arithmetical theory of 36
Limits, method of 37
Lindelof 124 125
Lindemann 81
Lines of invariability 326
Liouville 81 119
Locke 1
Loria 423
Lusin 108 180 182 29
Magnitude, theory of 20 53
Mahlo 131
Maxima and minima 283 326
Maxima and minima, of a function of two variables 416
Mean value theorem, of differential calculus 335
Mean value theorem, of integral calculus 564 652 660
Measure, exterior and interior 165
Measure, of limits of sequences of closed sets, Jordan's 183
Measure, of open and closed sets 159
Measure, of sets related to a system of sets 174
Measure, problem of 158
Measurement 52
Meray 22
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