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Bichteler K. — Integration Theory

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Название: Integration Theory

Автор: Bichteler K.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1973

Количество страниц: 357

Добавлена в каталог: 08.07.2008

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

Предметный указатель

      111
      31
$(\mathscr{R}, M)$       83
$(\mathscr{R}, M)-B$ -adequate fields      234
$a^B(\mathscr{J})$       19.14
$A^S(\mathscr{Y})$       19.13
$A_E^\infty$       256
      213
$C_{oo}(X)$       4
      253
      75
$E^{\mathscr{S}}$       29.8
, ,       48
$f^{*}$ , $g^{*}$       74
, F(M)      78
$I_+(\mathscr{F},R)$ , $I_O(\mathscr{F}, R)$       27
$I_O(\mathscr{F})$       28
$I_O(\mathscr{F}, E)$       30
$I_O(\mathscr{F}; E, R)$       37
$L_E^1=L_E^1(\mathscr{R},M)$       80
, ,       210 212
      2 7.16
$M^{*}(\mathscr{F})$       32
$M^{*}(\mathscr{F};E)$       33
$M^{*}(\mathscr{F};E,R)$       37
$m_1 \times m_2$       238—240
,       151
$M_b(\mathscr{R};F)$       13.12
      133
$m_\infty$       261
$m_{PS}$ , $m_{PL}$       33 17B
$S(\mathscr{F}$ , $S(\mathscr{R}))$       57
$T(\mathscr{R},M)$       173
      167
$U(\mathscr{F})$       52
$U(\mathscr{S})$       233
$U_\eta$ ,       49 116
      13
$X_\infty$ ,       57
      120
$\approx$       8.18
$\bot$       19 31
$\cdot$ , $(f^\cdot)$       74
$\check{}$       56
$\Delta$       51
$\delta_p$ , $\delta^{'}_p$       239
$\delta_x$       210
$\dot{=}$ , $\dot{\geq}$ (M)      74
$\hat{}$       54 56
$\hat{}$ , $\check{}$       12
$\int$       104 114
$\int^V$       117
$\int^\oplus$       82
$\int{LdM}$       226
$\langle; \rangle$       223 225
$\ll$       21 31 38 7.20 9.9
$\mathscr{B}^B(\mathscr{J})$       19.14
$\mathscr{B}^S(\mathscr{Y})$       19.13
$\mathscr{C}(\mathscr{R}, M)$       85
$\mathscr{C}(\mathscr{R}^B)$       92
$\mathscr{C}(\mathscr{R}^s)$       66
$\mathscr{D}_E[\mathscr{R}]$       41
$\mathscr{D}_T$       302
$\mathscr{D}_T^\infty$       303
$\mathscr{F}^S$       65
$\mathscr{F}^\Sigma$       72
$\mathscr{F}_E(M)$ , $\mathscr{F}(M)$       76
$\mathscr{K(R)}$ , $\mathscr{K(F)}$       41
$\mathscr{K}^S(\mathscr{R})$ , $\mathscr{K}^B(\mathscr{R})$ , $\mathscr{K}^{*}(\mathscr{R})$       64
$\mathscr{L}^1=\mathscr{L}^1(\mathscr{R},M)$       78
$\mathscr{L}_0^1$       8.19
$\mathscr{L}_E^1=\mathscr{L}_E^1(\mathscr{R},M)$       78
$\mathscr{L}_E^P=\mathscr{L}_E^P(\mathscr{R},M)$       136
$\mathscr{L}_E^\ell(\mathscr{R},M)$ , $L_E^\ell(\mathscr{R},M)$       198
$\mathscr{L}_E^\infty$ , $L_E^\infty$       185
$\mathscr{L}_E^{1V}$       117
$\mathscr{L}_Y(\mathscr{R},M)$       165
$\mathscr{M}_Y^\infty$       306
$\mathscr{N}_E(M)$ , $\mathscr{N}(M)$       78
$\mathscr{P}(\mathscr{R},M)$       156
$\mathscr{R}$ -topology      5.11
$\mathscr{R}$ -topology, vague      24.13
$\mathscr{R}$ -uniformity      5B
$\mathscr{R}/I$       22
$\mathscr{R}[K]$       42
$\mathscr{R}\otimes E$       42
$\mathscr{R}^B$ , $\mathscr{R}^B_{\uparrow\downarrow}$       92
$\mathscr{R}^B_\uparrow$ , $\mathscr{R}^S_\uparrow$ , $\mathscr{R}^{*}_\uparrow$ , $\mathscr{R}^{*}_\downarrow$       64 90
$\mathscr{R}^s$ , $(\mathscr{R}\otimes E)^S$       66
$\mathscr{R}_1 \times \mathscr{R}_2$       237
$\mathscr{R}_O$       42
$\mathscr{R}_\infty$       259
$\mathscr{S}(\mathbb{R})$       1
$\mathscr{S}(\varphi)$       5
$\mathscr{U}^B(\mathscr{R})$ , $\mathscr{U}^S(\mathscr{R})$ , $\mathscr{U}^{*}(\mathscr{R})$       64
$\mathscr{U}^{*}_0(\mathscr{R})$       9.6
$\mathscr{U}_b(\mathscr{F},\ )$       53
$\otimes \mathscr{R}_i$       285
$\overline{m^{*}}$ , $\overline{m^{*}}_P$       141
$\overline{M}$       138
$\overline{\mathscr{R}^U}$       5.3 58
$\overline{\mathscr{R}}$ , $\widehat{\mathscr{R}}$       59
$\overline{\mathscr{R}}_E$       43 59 61
$\phi \uparrow^{*} h$       32
$\pi:X\rightarrow \widehat{X}$       54 57
$\sigma$ -additive content      34
$\sigma$ -algebra (= tribe)      6.12
$\sigma$ -bounded measures      13.13
$\Sigma$ -closure      6.16
$\sigma$ -finite sets and upper gauges      13A 138
$\sigma(G,V)$       47
$\Theta_T$       305
$\underleftarrow{lim}$       258 261 270
$\underline{K}$       158
$\underline{x}$       158
$\underrightarrow{lim}$       40
$\vee$ , $\wedge$       14
$\widehat{m}$       17A
$\widehat{U}$       62
$\widehat{x}$       54
$\widetilde{S}$       56
$\|g\|m^{*-}$       22.8
$\|m^{*}\|$       9.1
$\|U\|$ , |U|      45
$\|U\|^{*}$       116 11.8
$\|\ \|$       45
'      47
( $\mathscr{R}$ , $\overline{M}$ )      138
(A),(n),(x)      18
*-continuity      3D 31
*-continuity is determined on a uniformly dense subspace      3.15
*-continuity of a product      27.3 32.1
*-continuity of an integral of a field      25.4
*-continuity, weak      4D
*-continuous elementary integrals      3D see
*-continuous, measures      3D 31 see
1      48
A(P)      247
Absolute continuity for Banach-valued measures      31
Absolute continuity for upper S-norms      7.20 see 15.8
Absolute continuity in a Riesz space      21
Absolute continuity, characterization for scalar measures      3.8 6.7 see 29A
Absolute continuity, uniform absolute continuity of linear maps on a convex set      119—120
Absolute value      13
Adapted maps      28B
Adequate cover by integrable sets      86 see
Adequate cover by measurable sets      170
Adequate field      26B
Adequate map      28A
Adequate partition      16A 156

Admissible function      252
Admissible topology      108
Algebra of sets      6 11
Almost compact measures      37A
Almost compact-valued functions      178
Almost everywhere (a.e.)      74
Almost separably-valued functions      178
AM      147
AU      153
B-continuous integral of a field      26A-B
B-continuous measure (= B-measure)      3D see 4.19
B-continuous part of a measure      3 11 17 3
B-continuous upper gauge      8C see 11.8
B-continuous upper gauge, associated with a lifting      34.1
B-continuous, weakly B-continuous linear maps      4D 11A 116
Baire category theorem      11.5
Baire functions and sets      6.16
Baire functions and sets, dominated      66 8.23
Baire functions and sets, equivalent to an integrable function      7.18
Baire measurable functions      19.13
Banach lattice      3E 36 see 10
Banach lattice with order-continuous norm      3E 36 see 9A 94
Banach space over a Banach lattice      3E 36 see
Band      18
Band decomposition of Riesz      2.18 see
Band of *-measures      3.10 3.11 3E
Band of diffuse, discrete, or tight measures      24C
Band, a band in a band is a band      2 24
Band, characterizations      2.20 2.21
Bauer's theory      17A see 10.7 24.1
Bochner integrable      78
Bochner integral      10A
Bochner integral of a weakly compact linear map      11C see
Borel functions and sets      18.21
Borel functions and sets, dominated      92 8.23
Borel measurability      19.14
Borel — Cantelli lemma      32.5
C(f)      178
C(n), C(n,M)      330
Caratheodory      19.D
ce(), $\overline{ce}()$       107
Chain rule      22.9
Character (space) of $L^\infty$       20B see
Character (space) of a family of functions      54
Clan (= ring of sets)      1B 5 see 6.1 "Full" "Extension" "Spectrum"
Clan of integrable sets      8.4
co(), $\overline{co}()$       106
Compact and $(\tau,M)$ -compact linear maps      10B
Compactness criterion for admissible topologies      10.6
Compactness of $L^{p^{'}}_F$       21.11
Compactness properties of the integral      10B
Completeness of $\mathscr{F}_E(M)$       7.9
Completeness of $\mathscr{L}_E^1$       7.12
Completeness of $\mathscr{L}_E^\infty$       20.3
Completeness of a Riesz space      17
Complex measures      3.14
Conditional distribution      36.10
Conditional expectation      29A-C
Conditional expectation under $\mathscr{S}$       29.8
Conjugate numbers      193
Content, elementary      1B 5
Content, elementary, extension      1.1 3.12 98
Content, elementary, S-continuous (= $\sigma$ -additive)      34
Continuity a.e. with respect to a lifting      34.8
Continuity of linear maps on $\mathscr{R}_E$       4.6
Convergence a.e.      74
Convergence at infinity      54
Convergence in mean      76
Convergence in measure      18.14 28.15
Convergence of a martingale      31A-D
Convergence of a martingale, locally in p-mean      31.2 31.11
Convergence of a martingale, pointwise      31D 31.11
Daniell integration      1A
Daniell integration, of linear maps      11C
Darboux property      24.12
Dense family of integrable sets      86
Dense family of integrable sets, examples      8.8 8.20 165
Dense subsets of $\mathscr{L}^1_E$       8.4
Dense topology      34B see
Dense, $\widehat{R_E}$ in $C_{ooE}(S(\mathscr{R}))$       5.3
density      34.11 see
Derivative, locally integrable      22A-B
Derivative, locally integrable, existence for almost weakly compact measures      37B
Derivative, locally integrable, existence for scalar measures      22.6 22.7
Derivative, scalarly locally integrable      37A
Dini's theorem      4 12
Dirac measure      24B
Direct integral of Banach spaces      7.22
Direct sum of Riesz spaces      20
Direct sum property      16.10
Discrete (= atomic) measures      210
Disintegration of a measure      36A
Disintegration of a support function      36.8
Disintegration of a tight measure      36.3
Disintegration, strong      36.3 see
Disjoint Banach-valued measures      3C 31 3.17
Disjoint elements of a Riesz space      19
Disjoint, characterization of disjoint scalar measures      3.8 6.6
distribution      28.15
dm/dn      198
Dominated Baire functions and sets      66
Dominated Borel functions and sets      92
Dominated functions and sets      4B
Dominated integration lattices      4.4
Dominated sets are precompact      5.4
Doob's martingale theorem      31.9
Dual of       21.6 21.7 31.7
Dual of       21.7 37.1
Dual of a Riesz space      28
E', F', G'      47
Egoroff's theorem      18.11
Elementary integral      1B 3
Elementary integral, *-continuous      3D 31
Elementary integral, associated with an elementary content      1.1 3.12
Elementary measure space      1B 3
Elementary measure space, *-continuous      31
Equi-tight measures      24.14
Equivalent functions modulo negligible ones      78
Equivalent upper gauges      8.18 see
Equivalent upper gauges are simultaneously tight      24.16
Equivalent upper gauges have the same dense dominated families      14.4
Equivalent upper gauges have the same essential sup-norm      20.2
Essential $\tau$ -open kernel      34.11
Essential essentially equal upper S-norms      7.15
Essential supremum norm      20A
Essential upper gauge      13A
Expectation      33A see
Extended reals      5A
Extension of an elementary content on a clan      1.1 3.12 98
Extension of an elementary integral under an upper norm      1A 10A
Extension of linear maps      11A 11C
Extension of the Riemann integral of step functions      1A
Fatou's lemma      8.11
Field of integrable variation      218
Field of linear maps      224
Field of measures and of upper gauges      25A-B 26A-C see
Field, adequate      26A-B
Field, integrable      25A
Field, tame      230
Finite sets and upper gauges      13A 138
Fubini's theorem      25.3 see 27.4 36.4
Full clan (= $\delta$ -ring)      66 67
Full integration domain      6B see 6C "S-measure"
Full projective system or limit      30A
Full span      6A
Gelfand transform of functions      5D
Gelfand — Bauer transform of measures      5D 17A-B see
gM, $\|g\|M$       199 15.9
gm, gn      70 197
Hahn's theorem      6.6 see 6.17

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