Real functions - current topics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1995
|
| Series: | Lecture notes in mathematics
1603 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 310 S. graph. Darst. |
| ISBN: | 3540600086 |
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MARC
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| 100 | 1 | |a Ene, Vasile |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Real functions - current topics |c Vasile Ene |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1995 | |
| 300 | |a XI, 310 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1603 | |
| 650 | 4 | |a Fonctions de variables réelles | |
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VASILE ENE REAL FUNCTIONS - CURRENT TOPICS SPRINGER CONTENTS 1
PRELIMINARIES 1 1.1 NOTATIONS 1 1.2 THE 6* DECOMPOSITION OF A SET 2 1.3
NOTIONS RELATED TO HAUSDORFF MEASURES. CONDITIONS /./. AND ER././. . 2
1.4 OSCILLATIONS 4 1.5 BOREL SETS F A , GS; BOREL FUNCTIONS; ANALYTIC
SETS 8 1.6 DENSITIES; FIRST CATEGORY SETS 9 1.7 THE BAIRE CATEGORY
THEOREM; ROMANOVSKI'S LEMMA 10 1.8 VITALI'S COVERING THEOREM 11 1.9 THE
GENERALIZED PROPERTIES PG, [PG], PI,P 2 G 11 1.10 EXTREME DERIVATIVES 13
1.11 APPROXIMATE CONTINUITY AND DERIVABILITY 14 1.12 SHARP DERIVATIVES
D*F 15 1.13 LOCAL SYSTEMS; EXAMPLES 16 1.14 5-OPEN SETS 19 1.15
SEMICONTINUITY; 5-SEMICONTINUITY 21 2 CLASSES OF FUNETIONS 25 2.1
DARBOUX CONDITIONS T , P_, 2 + 25 2.2 BAIRE CONDITIONS B\, BJ, B\ 27
2.3 CONDITIONS D; C*; [CIG]; [CG] 31 2.4 CONDITIONS INTERNAL, INTERNAL*,
ZI, UCM 33 2.5 CONDITIONS V-B X , VB X 36 2.6 CONDITIONS B\, WB\, 5J AND
$J-LOCAL SYSTEMS 39 2.7 CONDITIONS VB, VB, VBG 41 2.8 CONDITIONS VB*,
VB*, VB*G 44 2.9 CONDITIONS MONOTONE* AND VB* 47 2.10 CONDITIONS VB*,
VB*G AND V, IL, [CG], [CIG], LOWER INTERNAL, INTERNAL 50 2.11 CONDITIONS
AC, ACG, 51 2.12 CONDITIONS AC*, AC*, AC*G,AC_*G 54 2.13 CONDITIONS L,
L, LG, LG 58 2.14 SUMMABILITY AND CONDITIONS VB AND AC 60 2.15
DIFFERENTIABILITY AND CONDITIONS VBG, VB*G 62 2.16 A FUNDAMENTAL LEMMA
FOR MONOTONICITY 65 2.17 KRZYZEWSKI'S LEMMA AND FORAN'S LEMMA 70 2.18
CONDITIONS (N), T U T 2 , (S), (+), (-) 71 2.19 CONDITIONS WS, WN 78
VLLL CONTENTS 2.20 CONDITION (TV) 78 2.21 CONDITIONS N, N+, N~ 79
2.22 CONDITIONS M*,W_ 82 2.23 CONDITIONS (M), M, N*, N+ 84 2.24
DERIVATION BASES 87 2.25 CONDITIONS AC D #, AC D O, AC D 88 2.26
CONDITION Y D #, Y D , Y D 89 2.27 CHARACTERIZATIONS OF ACG N C,
AC*GNCI, AC AND AC 90 2.28 CONDITIONS AC N , AC U , AC X , T 93 2.29
CONDITIONS VB N , VB», VB^, B 96 2.30 VARIATIONS V N , K,, VX AND THE
BANACH INDICATRIX 100 2.31 CONDITIONS S*, WS 0 AND AC X VB X , (N) 103
2.32 CONDITIONS L N , L U , ,, C 104 2.33 CONDITIONS HZ, AZ, /./.,
A.F.L 108 2.34 CONDITIONS SAC N , SAC W , SAC^, SF 111 2.35 CONDITIONS
SVB N , SVB U , SVB^-.SB 114 2.36 CONDITIONS DW N , DW U , DW X , DW*
116 2.37 CONDITIONS E N , E U , E^, 118 2.38 CONDITIONS SAC, SACG,
SVB, SVBG, SY 121 3 FINITE REPRESENTATIONS FOR CONTINUOUS FUNCTIONS 127
3.1 QUASI-DERIVABLE C AC*; DWG+AC*; DWG AND APPROXIMATELY QUASI-
DERIVABLE C AC;DW 1 G + AC;DW L G 127 3.2 C C DWI + DWI ON A PERFECT
NOWHERE DENSE SET 130 3.3 WRINKLED FUNCTIONS (W) AND CONDITION (M) 131
3.4 C = QUASI-DERIVABLE + QUASI-DERIVABLE 134 3.5 C = AC*; DWRG + AC*;
DW^G + AC*; DW 1 G 135 4 MONOTONICITY 141 4.1 MONOTONICITY AND
CONDITIONS (*), VB U G, T ^B T 141 4.2 MONOTONICITY AND CONDITIONS
M.UCM.AC.C C*,T I 142 4.3 MONOTONICITY AND CONDITIONS N~; N 145 4.4
LOCAL MONOTONICITY 149 4.5 4.6 RELATIVE MONOTONICITY 151 4.7 AN
APPLICATION OF COROLLARY 4.4.1 151 4.8 A GENERAL MONOTONICITY THEOREM
152 4.9 MONOTONICITY IN TERMS OF EXTREME DERIVATIVES 158 5 INTEGRALS 161
5.1 DESCRIPTIVE AND PERRON TYPE DEFINITIONS FOR THE LEBESGUE INTEGRAL
. 161 5.2 WARD TYPE DEFINITIONS FOR THE LEBESGUE INTEGRAL 166 5.3
HENSTOCK VARIATIONAL DEFINITIONS FOR THE LEBESGUE INTEGRAL 167 5.4
RIEMANN TYPE DEFINITIONS FOR THE LEBESGUE INTEGRAL (THE MCSHANE
INTEGRAL) 169 5.5 THEOREMS OF MARCINKIEWICZ TYPE FOR THE LEBESGUE
INTEGRAL 172 5.6 BOUNDED RIEMANN* SUMS AND LOCALLY SMALL RIEMANN* SUMS
173 5.7 DESCRIPTIVE AND PERRON TYPE DEFINITIONS FOR THE 2?*-INTEGRAL 174
CONTENTS IX 5.8 AN IMPROVEMENT OF THE HAKE THEOREM 180 5.9 AN
IMPROVEMENT OF THE LOOMAN-ALEXANDROFF THEOREM. THE EQUIVALENCE OF THE
"-INTEGRAL AND THE ('PJ^-INTEGRAL 184 5.10 WARD TYPE DEFINITIONS FOR
THE X *-INTEGRAL 186 5.11 HENSTOCK VARIATIONAL DEFINITIONS FOR THE V-
INTEGRAL 187 5.12 THE KURZWEIL-HENSTOCK INTEGRAL 188 5.13 CAUCHY AND
HARNAK EXTENSIONS OF THE V* - INTEGRAL 189 5.14 A THEOREM OF
MARCINKIEWICZ TYPE FOR THE V*- INTEGRAL 190 5.15 BOUNDED RIEMANN SUMS
AND LOCALLY SMALL RIEMANN SUMS 192 5.16 RIEMANN TYPE INTEGRALS AND LOCAL
SYSTEMS 193 5.17 THE LPG AND LDG INTEGRALS 197 5.18 THE CHAIN
RULE FOR THE DERIVATIVE OF A COMPOSITE FUNCTION 200 5.19 THE CHAIN RULE
FOR THE APPROXIMATE DERIVATIVE OF A COMPOSITE FUNCTION . 202 5.20 CHANGE
OF VARIABLE FORMULA FOR THE LEBESGUE INTEGRAL 204 5.21 CHANGE OF
VARIABLE FORMULA FOR THE DENJOY* INTEGRAL 205 5.22 CHANGE OF VARIABLE
FORMULA FOR THE LDG INTEGRAL 206 5.23 INTEGRALS OF FORAN TYPE 207
5.24 INTEGRALS WHICH EXTEND BOTH, FORAN'S INTEGRAL AND ISEKI'S INTEGRAL
. 210 6 EXAMPLES 213 6.1 THE CANTOR TERNARY SET, A PERFECT NOWHERE
DENSE SET 213 6.2 THE CANTOR TERNARY FUNCTION TP 214 6.3 A REAL BOUNDED
6.4 AN B\ 215 6.5 A FUNCTION F C IT F $ C* 215 6.6 A FUNCTION F V, F
[C*G], F #[CG] 215 6.7 A FUNCTION F VB X , F 0 [C 6.8 A FUNCTION F
UCM; F G ICM 216 6.9 A FUNCTION CONCERNING CONDITIONS T +, 2?_, CM, SCM,
LOWER INTERNAL . 217 6.10 A FUNCTION CONCERNING CONDITIONS: 2 _, T ,
INTERNAL, B_I, B\, B\, WB\, [VBG], (-), T U T 2 (BRUECKNER) . . * 217
6.11 A FUNCTION CONCERNING CONDITIONS: B\, BJ , Z _ , +, LOWER
INTERNAL, INTERNAL, INTERNAL* (DIRICHLET) 218 6.12 A FUNCTION CONCERNING
CONDITIONS: V, V-, B\, C{, C*, LOWER INTERNAL, INTERNAL*, VB, VB*G,
N-_ J_ * *_: 219 6.13 A FUNCTION F V, F GB, \ SS X ; -F * , \ C U -F
E V_B X \Z T . 219 6.14 A FUNCTION I ? EB 1 \F 1 ,F* LOWER INTERNAL,
F XL 220 6.15 A FUNCTION F * SCM, F 0 INTERNAL* 220 6.16 A FUNCTION F
6 AC'G\ AC, FEC?\T ,F E SCM\ INTERNAL* 220 6.17 A FUNCTION F G (D.C.), F
* BI, F G M 2 , F 221 6.18 A FUNCTION FE(+)N (-); F $ VBIT 2 221 6.19 A
FUNCTION G 6 V, G ^BJ, G & B X , G' AP (X) EXISTS N.E., G' AP (X) 0
O.E. (PREISS) ._. 222 6.20 A FUNCTION H * 2?, H BI, H GFII, H' AP (X)
EXISTS ON (0,1) (PREISS) . . 222 6.21 A FUNCTION F VB U F(X) = 0 O.E.,
F IS NOT IDENTICALLY ZERO (CROFT) . . 223 6.22 A FUNCTION F V, F G
[CG], F [VBG], F $ VB*G, F&C (BRUCKNER)223 6.23 A FUNCTION F AC, F
VB* 224 X CONTENTS 6.24 A FUNCTION F G C, F G T X , F G VBG, F $ VB*G
224 6.25 A FUNCTION F G [BACG] D VB*GNN- F G LOWER INTERNAL 225 6.26 A
FUNCTION F G C D (S) N LG, F AC*G, F'{X) DOES NOT EXIST ON A SET OF
POSITIVE MEASURE, F(X) + X G LG, F(X) + X T X 225 6.27 A FUNCTION F G
(S) D C SUCH THAT THE SUM OF F AND ANY LINEAR NONCON- STANT FUNCTION
DOES NOT SATISFY (N) (MAZURKIEWICZ) 226 6.28 A FUNCTION F G (M), F#T 2
227 6.29 FUNCTIONS CONCERNING CONDITIONS (M), AC, T X , T 2 , (S), (TV),
L, L 2 G, VBG, ST, QUASI-DERIVABLE 229 6.30 A FUNCTION G G N, F $ (M),
F (+) 237 6.31 FUNCTIONS CONCERNING CONDITIONS (S), (N), (M), TI, T 2 ,
ACG, AC N , SACN, VB 2 , VBG, SVB, T, ST 238 6.32 A FUNCTION F G LOWER
SEMICONTINUOUS, F G AC 2 , F AC 244 6.33 A FUNCTION F N G -L*+I ON A
PERFECT SET, F N G VB N ON NO PORTION OF THIS SET, F N G L N+ IG, F N &
AC N G ON [0,1] 245 6.34 FUNCTIONS F G L 2 G, G, G (N), G' 5 = F' O.E.,
G, - F IS NOT IDENTICALLY ZERO, F SACG 247 6.35 A FUNCTION F GLA, F#T
2 ,F#B 250 6.36 A FUNCTION F G VB 2 ON C, V 2 {F; C) 1 252 6.37 A
FUNCTION F P G L V , F P $ AC V - X , F P G VB 2 ON C; V 2 (F P ; C) 1
. 252 6.38 A FUNCTION G G VB 2 , G $ AC N ON C, G G ^ ON [0,1] 254
6.39 A FUNCTION F X G V 2 ON C, V 2 {FUE [0,X] FLC) = P(X) (G. ENE) 254
6.40 A FUNCTION F, G (N) ON [0,1], F, V N ON C, F, G VB U ON C (G.
ENE)255 6.41 A FUNCTION G, G XZG, G! ET,G T ^ SVBG, G T I SACG, {GI)' AP
DOES NOT EXIST ON A SET OF POSITIVE MEASURE 256 6.42 A FUNCTION F G
SACG, F$T,F$ ACG 258 6.43 A FUNCTION F G DWI, F $ DW* 261 6.44 A
FUNCTION F G AC*;DW X G, F # AC*;DW'G 261 6.45 FUNCTIONS F U F 2 G C L~L
AC*;DW*G, F X ,F 2 ARE DERIVABLE O.E., F[ = F2 O.E., FI AND F 2 DO NOT
DIFFER BY A CONSTANT 262 6.46 FUNCTIONS FI,F 2 G CNAC*;DW X G, F X , F 2
ARE APPROXIMATELY DERIVABLE O.E., FI + F 2 ^ QUASI-DERIVABLE 262 6.47
FUNCTIONS FI,F 2 G SHB, F U F 2 T, F X + F 2 G 264 6.48 A FUNCTION
G* G F*+I, G N ^ E N , G N G_L N 2 +2N+1 , G N $ VB N 2 +2N . 265
6.49 FUNCTIONS CONCERNING CONDITIONS L,F,.F, VB 2 G, B, E X G 268 6.50 A
FUNCTION F G S H VB U G, F#B 270 6.51 A FUNCTION F G (N), F 0 AZ (FORAN)
271 6.52 A FUNCTION F G AC O AZ, F $ AZ (FORAN) 272 6.53 A FUNCTION H G
AC + AZ, H $ AZ (FORAN) 272 6.54 A FUNCTION G G AC * AZ, G & AZ (FORAN)
272 6.55 A FUNCTION F X G AC, F, L N , F X & C 273 6.56 FUNCTIONS FI G
AC 2 G, F 2 G AZ, F X + F 2 (M), F; = -F 2 ' O.E 273 6.57 A FUNCTION F
G AZ, F $ [S] 274 6.58 FUNCTIONS F X G (5), FI G AC O A.F.L, F X $
A.F.L, F 2 G L, F X + F 2 2 276 6.59 FUNCTIONS G X G A.F.L, G 2 G AC, G
X + G 2 $ A.F.L 279 6.60 FUNCTIONS H X G A.F.L, H 2 G AC, H X * H 2 $
A.F.L 280 CONTENTS XI 6.61 A FUNCTION F E CR.F.L., F 6 7I, F B, F IS
NOWHERE APPROXIMATELY DERIVABLE, (FORAN) 280 6.62 A FUNCTION G 6
CR.F.L., G * T\, G IS NOWHERE DERIVABLE, G' AP (X) = 0 A.E., G $ W, G *
W* (FORAN) 284 6.63 A FUNCTION F W ON A PERFECT NOWHERE DENSE SET OF
POSITIVE MEASURE, WITH EACH LEVEL SET PERFECT, F IS NOWHERE
APPROXIMATELY DERIVABLE . 287 6.64 A FUNCTION G\ G DW\ FLC, G\ IS NOT
APPROXIMATELY DERIVABLE O.E. ON A SET OF POSITIVE MEASURE 291 6.65 A
FUNCTION F * C, F IS QUASI-DERIVABLE, F AC O AC + AC 291 6.66 EXAMPLES
CONCERNING THE CHAIN RULE FOR THE APPROXIMATE DERIVATIVE OF A COMPOSITE
FUNCTION 291 BIBLIOGRAPHY 293 INDEX 305 |
| any_adam_object | 1 |
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| id | DE-604.BV010194794 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:09Z |
| institution | BVB |
| isbn | 3540600086 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006774504 |
| oclc_num | 845022215 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-706 DE-83 DE-11 DE-188 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-706 DE-83 DE-11 DE-188 |
| physical | XI, 310 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Ene, Vasile Verfasser aut Real functions - current topics Vasile Ene Berlin u.a. Springer 1995 XI, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1603 Fonctions de variables réelles Fonctions réelles ram Reële functies gtt Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s DE-604 Lecture notes in mathematics 1603 (DE-604)BV000676446 1603 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006774504&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ene, Vasile Real functions - current topics Lecture notes in mathematics Fonctions de variables réelles Fonctions réelles ram Reële functies gtt Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd |
| subject_GND | (DE-588)4048918-8 |
| title | Real functions - current topics |
| title_auth | Real functions - current topics |
| title_exact_search | Real functions - current topics |
| title_full | Real functions - current topics Vasile Ene |
| title_fullStr | Real functions - current topics Vasile Ene |
| title_full_unstemmed | Real functions - current topics Vasile Ene |
| title_short | Real functions - current topics |
| title_sort | real functions current topics |
| topic | Fonctions de variables réelles Fonctions réelles ram Reële functies gtt Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd |
| topic_facet | Fonctions de variables réelles Fonctions réelles Reële functies Functions of real variables Reelle Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006774504&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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