Leader S. — The Kurzweil-Henstock integral and its differentials :: Электронная библиотека попечительского совета мехмата МГУ

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Leader S. — The Kurzweil-Henstock integral and its differentials

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Название: The Kurzweil-Henstock integral and its differentials

Автор: Leader S.

Аннотация:

Timely reference and text providing a comprehensive review of the Kurzweil-Henstock integrations process on the real line and on higher dimensions. Presents a unified theory of integrations that highlights integrals of elementary calculus, Lebesque integrals and other methods.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 371

Добавлена в каталог: 18.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\delta$ -division      12
$\delta$ -fine      12
$\delta$ -neighborhood      12
$\delta$ -sum (lower/upper)      16 17
$\mathcal{Q}$ (orientation summant)      16 25 196
$\sigma$ -essentials limits      223
$\sigma$ -everywhere      73
$\sigma$ -null      73 126
Abutting cells      9
Additive      21 342
Approximating sums      16
Banach indicatrix      267 272
Banach lattice      341
Banach space      328
Boolean algebras/fields      10
Borel sets      130
Boundary      326 331
Bounded sets      323
Cauchy extension      6
Cauchy integral      2
Cauchy sequence      324
Cauchy — Schwarz inequality      329
cell      9
Cell interior      9 285
Cell summant      15 21
Cell, tagged      11
Closed, closure      326 331
Cluster point      332
Cofinal sets      319
Complete metric space      324
Component, connected      332
Continuity      96 324 332
Continuity, absolute      249 250 251 258
Continuity, left/right      181
Continuity, uniform      324
Continuity, uniform absolute      263 265
Convergence      332
Convex      330
Cousin's lemma      13
Damper      92 99
Diameter      323
Differentiable functions      187
Differential      3 6 53
Differential coefficient      6 73 187
Differential convergence      57
Differential equivalence      53
Differential norm      57
Differential of a function      66
Differential, absolutely integrable      60
Differential, archimedean differential      99
Differential, conditionally integrable      60
Differential, continuous      96
Differential, dampable      99
Differential, damper-summable      99
Differential, idempotent      92
Differential, Stieltjes      77
Differential, summable      58
Differential, tag-finite      87
Differential, unit differential $\omega$       6 91
Dini derivatives      61
Directed set      321
Division      11
Essential boundedness      235
Essential continuity      238
Essential infimum/supremum      235
Essential lower/upper bounds      235
Essential variation      241
Exterior      326 331
Extreme point      330
figure      9
Filter      319
Filter base      319

Filter, ultra      319
Frequently      319
Gauge      11
Gradient      187
Hahn decomposition      133
Hilbert space      328
Indicator      10
Inner product      187 328 329
Integrable      18 54
Integrable, uniformly      33 36
integral      1—6 18 53 54
Interior      9 285 326 331
Invariants      324
Lebesgue space $\mathcal{L}_{1}$       78
Limits (lower/upper)      320
Measurable      129—131 137 139
Measure      145
Measure, Lebesgue measure      132
Measure, outer measure      169
Metric      322
n-cell      285
n-cell, lower/upper faces      291
n-cell, vertex      285
n-differential      125 286
n-summant      125
Neigborhood      331
Net      321
Nonexpansive mapping      327
Norm      327 328
Nowhere dense set      334
Open set      331
Orientation summant $\mathcal{Q}$       16 25 196
Overlapping cells/figures      9
Path      303 304
Path, initial/terminal point of      304
Path, length of      304
Path, parametrized      303
Path, Polygonal      308
Path, rectifiable      304
Path, weakly archimedean      307
Product topology      333
Region      307
Regular closed set      9 335
Regular closure      335
Regular open set      335
Regulated function      145
Riesz homomorphism      340
Riesz ideal      340
Riesz norm      341
Riesz space      339
Sigma algebra      129
Simple arc      305
Simple closed curve      306
Solid set      55 340
Step function      145
Stone space      345
Summant      15
Summant, additive      21
Summant, cell      15 21
Summant, Stieltjes      16
Summant, sub/superadditive      22
Summant, tame      99
Terminal set      319
Topological equivalence      325
Topological space      339
Totally bounded set      325
Ultimate lower/upper bound      320
Ultimately      319
Uniform equivalence      324
Uniformly discrete set      325
Variation, bounded/unbounded      68
Variation, total      68
Vertex of n-cell      285

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