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Hobson E.W. — Theory of Functions of a Real Variable and the Theory of Fourier's Series V1
Hobson E.W. — Theory of Functions of a Real Variable and the Theory of Fourier's Series V1

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Название: Theory of Functions of a Real Variable and the Theory of Fourier's Series V1

Автор: Hobson E.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 688

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\eta, \theta, \pi$      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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