Real analysis: measure and integration
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
De Gruyter
[2019]
|
| Schriftenreihe: | De Gruyter graduate
|
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110600971&searchTitles=true Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XV, 339 Seiten Illustrationen 24 cm, 678 g |
| ISBN: | 9783110600971 3110600978 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV046105415 | ||
| 003 | DE-604 | ||
| 005 | 20210927 | ||
| 007 | t | ||
| 008 | 190815s2019 gw a||| |||| 00||| eng d | ||
| 015 | |a 19,A30 |2 dnb | ||
| 016 | 7 | |a 1172363382 |2 DE-101 | |
| 020 | |a 9783110600971 |c Broschur : EUR 64.95 (DE), EUR 64.95 (AT) |9 978-3-11-060097-1 | ||
| 020 | |a 3110600978 |9 3-11-060097-8 | ||
| 035 | |a (OCoLC)1121482378 | ||
| 035 | |a (DE-599)DNB1172363382 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-703 |a DE-634 |a DE-20 |a DE-1050 |a DE-11 | ||
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| 084 | |a SK 420 |0 (DE-625)143238: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Markin, Marat V. |e Verfasser |0 (DE-588)1169968635 |4 aut | |
| 245 | 1 | 0 | |a Real analysis |b measure and integration |c Marat V. Markin |
| 264 | 1 | |a Berlin |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XV, 339 Seiten |b Illustrationen |c 24 cm, 678 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter graduate | |
| 650 | 0 | 7 | |a Reelle Analysis |0 (DE-588)4627581-2 |2 gnd |9 rswk-swf |
| 653 | |a Fachhochschul-/Hochschulausbildung | ||
| 653 | |a Lebesgue-Integral | ||
| 653 | |a Lp-Raum | ||
| 653 | |a Maßtheorie | ||
| 653 | |a Messbare Funktion | ||
| 653 | |a Reelle Analysis | ||
| 689 | 0 | 0 | |a Reelle Analysis |0 (DE-588)4627581-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-060099-5 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-059882-7 |
| 856 | 4 | 2 | |m X:MVB |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110600971&searchTitles=true |
| 856 | 4 | 2 | |m B:DE-101 |q application/pdf |u http://d-nb.info/1172363382/04 |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031486133&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-031486133 | ||
Datensatz im Suchindex
| _version_ | 1804180415982862336 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
1
1.1
1.1.1
1.1.2
1.2
1.3
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.4.5
1.4.6
1.4.7
1.4.8
1.4.9
PRELIMINARIES
*
1
SET
THEORETIC
BASICS
*
1
SOME
TERMINOLOGY
AND
NOTATIONS
*
1
CARDINALITY
AND
COUNTABILITY
*
4
TERMINOLOGY
RELATED
TO
FUNCTIONS
*
6
UPPER
AND
LOWER
LIMITS
*
8
FUNDAMENTALS
OF
METRIC
SPACES
*
9
DEFINITION
AND
EXAMPLES
*
9
CONVERGENCE
*
10
COMPLETENESS
*
12
BALLS
AND
BOUNDEDNESS
*
13
INTERIOR
POINTS,
OPEN
SETS
*
15
LIMIT
POINTS,
CLOSED
SETS
*
16
DENSE
SETS
AND
SEPARABLE
SPACES
*
18
COMPACTNESS
*
19
CONTINUITY
*
22
2
2.1
2.2
2.3
2.4
2.5
2.5.1
2.5.2
2.5.3
2.6
BASIC
SET
CLASSES
*
25
SEMIRINGS,
SEMI-ALGEBRAS
*
25
RINGS,
ALGEBRAS
*
26
O-RINGS,
O-ALGEBRAS
*
29
MONOTONE
CLASSES
*
31
GENERATED
SET
CLASSES
*
32
INTERSECTION
LEMMA
*
33
GENERATED
SET
CLASSES
*
34
BOREL
SETS
*
39
PROBLEMS
*
40
3
3.1
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
MEASURES
*
43
SET
FUNCTIONS
*
43
MEASURE
*
45
DEFINITION
AND
EXAMPLES
*
45
PROPERTIES
OF
MEASURE
*
46
CONTINUITY
OF
MEASURE
*
49
MORE
EXAMPLES
OF
MEASURES
*
51
PROBLEMS
*
62
XII
CONTENTS
4
EXTENSION
OF
MEASURES
*
65
4.1
EXTENSION
OF
A
SET
FUNCTION
*
65
4.2
EXTENSION
FROM
A
SEMIRING
*
65
4.3
OUTER
MEASURE
*
68
4.3.1
DEFINITION
AND
EXAMPLES
*
68
4.3.2
CONSTRUCTION
OF
OUTER
MEASURES
*
69
4.4
P*-MEASURABLE
SETS,
CARATHEODORY
*
S
THEOREM
*
72
4.4.1
//*
-MEASURABLE
SETS
*
72
4.4.2
CARATHEODORY
*
S
THEOREM
*
74
4.5
COMPLETENESS
*
77
4.5.1
NULL
SETS,
COMPLETENESS
*
77
4.5.2
ADDENDUM
TO
CARATHEODORY
*
S
THEOREM
*
78
4.5.3
COMPLETION
*
79
4.6
MEASURE
EXTENSION
FROM
A
RING
*
81
4.6.1
CARATHEODORY
*
S
EXTENSION
THEOREM
*
82
4.6.2
APPROXIMATION
*
90
4.7
LEBESGUE-STIELTJES
MEASURES
*
92
4.7.1
THE
CONSTRUCT
*
92
4.7.2
RELATIONSHIPS
BETWEEN
VARIOUS
EXTENSIONS
OF
LENGTH
*
95
4.7.3
EXISTENCE
OF
A
NON-LEBESGUE
MEASURABLE
SET
IN
R
*
96
4.7.4
MULTIDIMENSIONAL
LEBESGUE
MEASURE
*
98
4.8
PROBLEMS
*
100
5
MEASURABLE
FUNCTIONS
*
105
5.1
MEASURABLE
SPACE
AND
MEASURE
SPACE
*
105
5.2
DEFINITION
AND
EXAMPLES
*
105
5.3
A
CHARACTERIZATION
OF
Z-Z -MEASURABILITY
*
107
5.4
BOREL
AND
LEBESGUE
MEASURABLE
FUNCTIONS
*
108
5.5
PROPERTIES
OF
MEASURABLE
FUNCTIONS
*
110
5.5.1
COMPOSITIONS
OF
MEASURABLE
FUNCTIONS
*
110
5.5.2
COMBINATIONS
OF
MEASURABLE
FUNCTIONS
*
111
5.5.3
SEQUENCES
OF
MEASURABLE
FUNCTIONS
*
112
5.6
SIMPLE
FUNCTIONS
*
114
5.7
LUZIN
*
S
THEOREM
-----
120
5.8
NOTION
OF
ALMOST
EVERYWHERE
*
124
5.8.1
DEFINITION
AND
EXAMPLES
*
124
5.8.2
EQUIVALENCE
OF
FUNCTIONS
*
125
5.8.3
A.
E.
CHARACTERIZATION
OF
MEASURABILITY
*
126
5.9
CONVERGENCE
ALMOST
EVERYWHERE
*
128
5.9.1
DEFINITION,
EXAMPLES,
AND
PROPERTIES
*
128
5.9.2
UNIQUENESS
A.
E.
OF
LIMIT
A.
E.
*
132
5.9.3
MEASURABILITY
OF
LIMIT
A.
E.
*
133
CONTENTS
*
XIII
5.9.4
EGOROV S
THEOREM
*
134
5.10
CONVERGENCE
IN
MEASURE
*
137
5.10.1
DEFINITION,
EXAMPLES,
AND
PROPERTIES
*
137
5.10.2
UNIQUENESS
A.
E.
OF
LIMIT
IN
MEASURE
*
140
5.10.3
LEBESGUE
AND
RIESZ
THEOREMS
*
141
5.11
PROBABILISTIC
TERMINOLOGY
*
145
5.12
PROBLEMS
*
145
6
ABSTRACT
LEBESGUE
INTEGRAL
*
151
6.1
DEFINITIONS
AND
EXAMPLES
*
151
6.2
PROPERTIES
OF
LEBESGUE
INTEGRAL
*
160
6.3
COUNTABLE
ADDITIVITY
*
165
6.4
FURTHER
PROPERTIES
*
167
6.5
MONOTONE
CONVERGENCE
THEOREM
*
173
6.6
LINEARITY
OF
LEBESGUE
INTEGRAL
*
177
6.7
BASIC
LIMIT
THEOREMS
-----
180
6.7.1
LEVI
*
S
THEOREM
*
180
6.7.2
FATOU
*
S
LEMMA
-----
182
6.7.3
LEBESGUE
*
S
DOMINATED
CONVERGENCE
THEOREM
*
184
6.8
CHANGE
OF
VARIABLE
THEOREM
*
186
6.9
APPROXIMATION
BY
CONTINUOUS
FUNCTIONS
*
188
6.10
COMPARISON
OF
RIEMANN
AND
LEBESGUE
INTEGRALS
*
192
6.10.1
RIEMANN
INTEGRAL
BASICS
*
192
6.10.2
CHARACTERIZATION
OF
RIEMANN
INTEGRABILITY
*
194
6.10.3
IMPROPER
INTEGRALS
AND
LEBESGUE
INTEGRAL
*
200
6.11
PROBLEMS
*
204
7
L
P
SPACES
*
211
7.1
HOLDER
*
S
AND
MINKOWSKI
*
S
INEQUALITIES
*
211
7.1.1
CONJUGATE
INDICES
*
211
7.1.2
TWO
IMPORTANT
INEQUALITIES
*
212
7.1.3
ESSENTIAL
SUPREMUM
*
213
7.1.4
P-NORMS
-----
215
7.1.5
HOLDER
*
S
INEQUALITY
*
217
7.1.6
MINKOWSKI
*
S
INEQUALITY
-----
219
7.2
CONVERGENCE
IN
P-NORM
*
221
7.2.1
DEFINITIONS
AND
EXAMPLES
*
221
7.2.2
CONVERGENCE
IN
OO-NORM
-----
224
7.2.3
UNIQUENESS
A.
E.
OF
LIMIT
IN
P-NORM
*
225
7.2.4
RELATIONSHIPS
BETWEEN
DIFFERENT
TYPES
OF
CONVERGENCE
*
225
7.3
FUNDAMENTALS
OF
NORMED
VECTOR
SPACES
*
226
7.3.1
DEFINITIONS
AND
EXAMPLES
*
226
XIV
*
CONTENTS
7.3.2
7.4
7.4.1
7.4.2
7.4.3
7.4.4
7.4.5
7.5
INCOMPLETENESS
OF
R[A,
B]
*
230
L
P
SPACES
*
233
DEFINITION
*
233
IMPORTANT
PARTICULAR
CASES
*
235
HOLDER
*
S
AND
MINKOWSKI
*
S
INEQUALITIES
IN
L
P
SPACES
*
236
COMPLETENESS
OF
L
P
SPACES
*
236
APPROXIMATION
IN
L
P
SPACES
*
241
PROBLEMS
*
245
8
8.1
8.2
8.3
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.3.6
8.4
8.4.1
8.4.2
8.4.3
8.4.4
8.5
8.5.1
8.5.2
8.5.3
8.5.4
8.5.5
8.5.6
8.6
DIFFERENTIATION
AND
INTEGRATION
*
249
DERIVATIVE
NUMBERS
*
249
VITALI
COVERS
AND
VITALI
COVERING
LEMMA
*
251
MONOTONE
FUNCTIONS
*
257
DEFINITION
AND
CERTAIN
PROPERTIES
*
257
TOTAL
JUMP
AND
JUMP
FUNCTION
*
258
DERIVATIVE
NUMBERS
OF
INCREASING
FUNCTIONS
*
261
DIFFERENTIABILITY
OF
MONOTONE
FUNCTIONS
*
269
TOTAL
CHANGE
ESTIMATE
*
270
THE
CANTOR
FUNCTION
*
272
FUNCTIONS
OF
BOUNDED
VARIATION
*
274
DEFINITION,
EXAMPLES,
PROPERTIES
*
274
ADDITIVITY
OF
TOTAL
VARIATION,
TOTAL
VARIATION
FUNCTION
*
278
JORDAN
DECOMPOSITION
THEOREM
*
279
DERIVATIVE
OF
A
FUNCTION
OF
BOUNDED
VARIATION
*
280
ABSOLUTELY
CONTINUOUS
FUNCTIONS
*
281
DEFINITION,
EXAMPLES,
PROPERTIES
*
281
CHARACTERIZATION
OF
ABSOLUTE
CONTINUITY
*
283
DERIVATIVE
OF
AN
ABSOLUTELY
CONTINUOUS
FUNCTION
*
286
SINGULAR
FUNCTIONS
*
287
ANTIDERIVATIVE
AND
TOTAL
CHANGE
FORMULA
*
289
LEBESGUE
DECOMPOSITION
THEOREM
*
292
PROBLEMS
*
294
9
9.1
9.2
9.3
9.3.1
9.3.2
9.3.3
9.4
9.4.1
SIGNED
MEASURES
*
297
DEFINITION
AND
EXAMPLES
*
297
ELEMENTARY
PROPERTIES
*
299
HAHN
DECOMPOSITION
*
300
POSITIVE,
NEGATIVE,
AND
NULL
SET
*
300
NEGATIVE
SUBSET
LEMMA
*
301
HAHN
DECOMPOSITION
THEOREM
*
303
JORDAN
DECOMPOSITION
THEOREM
*
306
MUTUAL
SINGULARITY
OF
MEASURES
*
306
CONTENTS
*
XV
9.4.2
9.4.3
9.5
9.5.1
9.5.2
9.5.3
9.6
9.7
JORDAN
DECOMPOSITION
THEOREM
*
307
TOTAL
VARIATION
OF
A
SIGNED
MEASURE
*
309
RADON-NIKODYM
THEOREM
*
309
ABSOLUTE
CONTINUITY
OF
SIGNED
MEASURE
*
309
RADON-NIKODYM
THEOREM
*
312
RADON-NIKODYM
DERIVATIVE
*
317
LEBESGUE
DECOMPOSITION
THEOREM
*
317
PROBLEMS
*
318
A
A.L
A.1.1
A.L.
2
A.1.3
A.2
A.3
THE
AXIOM
OF
CHOICE
AND
EQUIVALENTS
*
321
THE
AXIOM
OF
CHOICE
*
321
THE
AXIOM
OF
CHOICE
*
321
CONTROVERSY
*
321
TIMELINE
*
322
ORDERED
SETS
*
322
EQUIVALENTS
*
326
BIBLIOGRAPHY
*
331
INDEX
*
333
|
| any_adam_object | 1 |
| author | Markin, Marat V. |
| author_GND | (DE-588)1169968635 |
| author_facet | Markin, Marat V. |
| author_role | aut |
| author_sort | Markin, Marat V. |
| author_variant | m v m mv mvm |
| building | Verbundindex |
| bvnumber | BV046105415 |
| classification_rvk | SK 420 |
| ctrlnum | (OCoLC)1121482378 (DE-599)DNB1172363382 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV046105415 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:35:24Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110600971 3110600978 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031486133 |
| oclc_num | 1121482378 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-20 DE-1050 DE-11 |
| owner_facet | DE-703 DE-634 DE-20 DE-1050 DE-11 |
| physical | XV, 339 Seiten Illustrationen 24 cm, 678 g |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Markin, Marat V. Verfasser (DE-588)1169968635 aut Real analysis measure and integration Marat V. Markin Berlin De Gruyter [2019] © 2019 XV, 339 Seiten Illustrationen 24 cm, 678 g txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Reelle Analysis (DE-588)4627581-2 gnd rswk-swf Fachhochschul-/Hochschulausbildung Lebesgue-Integral Lp-Raum Maßtheorie Messbare Funktion Reelle Analysis Reelle Analysis (DE-588)4627581-2 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-060099-5 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059882-7 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110600971&searchTitles=true B:DE-101 application/pdf http://d-nb.info/1172363382/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031486133&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markin, Marat V. Real analysis measure and integration Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 |
| title | Real analysis measure and integration |
| title_auth | Real analysis measure and integration |
| title_exact_search | Real analysis measure and integration |
| title_full | Real analysis measure and integration Marat V. Markin |
| title_fullStr | Real analysis measure and integration Marat V. Markin |
| title_full_unstemmed | Real analysis measure and integration Marat V. Markin |
| title_short | Real analysis |
| title_sort | real analysis measure and integration |
| title_sub | measure and integration |
| topic | Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Reelle Analysis |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110600971&searchTitles=true http://d-nb.info/1172363382/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031486133&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT markinmaratv realanalysismeasureandintegration AT walterdegruytergmbhcokg realanalysismeasureandintegration |
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