Measure theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Graduate texts in mathematics
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 210 S. |
| ISBN: | 0387940553 3540940553 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV008879684 | ||
| 003 | DE-604 | ||
| 005 | 20000518 | ||
| 007 | t| | ||
| 008 | 940209s1994 xxu |||| 00||| engod | ||
| 016 | 7 | |a 940397005 |2 DE-101 | |
| 020 | |a 0387940553 |9 0-387-94055-3 | ||
| 020 | |a 3540940553 |9 3-540-94055-3 | ||
| 035 | |a (OCoLC)320301876 | ||
| 035 | |a (DE-599)BVBBV008879684 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-355 |a DE-12 |a DE-19 |a DE-824 |a DE-29T |a DE-91 |a DE-91G |a DE-703 |a DE-20 |a DE-521 |a DE-634 |a DE-83 |a DE-188 | ||
| 050 | 0 | |a QA325.D66 1994 | |
| 080 | |a 519.2 | ||
| 082 | 0 | |a 515/.42 20 | |
| 084 | |a SK 430 |0 (DE-625)143239: |2 rvk | ||
| 084 | |a 28-01 |2 msc | ||
| 084 | |a MAT 280f |2 stub | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 60Bxx |2 msc | ||
| 084 | |a 60A10 |2 msc | ||
| 100 | 1 | |a Doob, Joseph L. |d 1910-2004 |e Verfasser |0 (DE-588)12778022X |4 aut | |
| 245 | 1 | 0 | |a Measure theory |c J. L. Doob |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XII, 210 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 143 | |
| 650 | 4 | |a Measure theory | |
| 650 | 4 | |a Probabilities | |
| 650 | 0 | 7 | |a Maßtheorie |0 (DE-588)4074626-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Maßtheorie |0 (DE-588)4074626-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 143 |w (DE-604)BV000000067 |9 143 | |
| 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=005873364&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005873364 | |
Datensatz im Suchindex
| _version_ | 1820595315450839040 |
|---|---|
| adam_text |
J.L. DOOB
MEASURE THEORY
SPRINGER
CONTENTS
INTRODUCTION V
0. CONVENTIONS AND NOTATION 1
1.
NOTATION: EUCLIDEAN SPACE 1
2.
OPERATIONS INVOLVING
1
3.
INEQUALITIES AND INCLUSIONS 1
4.
A SPACE AND ITS SUBSETS 1
5.
NOTATION: GENERATION OF CLASSES OF SETS 2
6. PRODUCT SETS 2
7.
DOT NOTATION FOR AN INDEX SET 2
8. NOTATION: SETS DEFINED BY CONDITIONS ON FUNCTIONS 2
9. NOTATION: OPEN AND CLOSED SETS 3
10.
LIMIT OF A FUNCTION AT A POINT 3
11.
METRIC SPACES 3
12.
STANDARD METRIC SPACE THEOREMS 3
13.
PSEUDOMETRIC SPACES 5
1.
OPERATIONS ON SETS
I
1.
UNIONS AND INTERSECTIONS 7
2.
THE SYMMETRIC DIFFERENCE OPERATOR
A
7
3.
LIMIT OPERATIONS ON SET SEQUENCES 8
4.
PROBABILISTIC INTERPRETATION OF SETS AND OPERATIONS ON THEM 10
II.
CLASSES OF SUBSETS OF A SPACE 11
1.
SET ALGEBRAS 11
2.
EXAMPLES 12
3.
THE GENERATION OF SET ALGEBRAS 13
4.
THE BOREL SETS OF A METRIC SPACE 13
5.
PRODUCTS OF SET ALGEBRAS 14
6. MONOTONE CLASSES OF SETS 15
VIII MEASURE THEORY
III.
SET FUNCTIONS
17
1.
SET FUNCTION DEFINITIONS 17
2.
EXTENSION OF A FINITELY ADDITIVE SET FUNCTION 19
3.
PRODUCTS OF SET FUNCTIONS 20
4.
HEURISTICS ON A ALGEBRAS AND INTEGRATION 21
5.
MEASURES AND INTEGRALS ON A COUNTABLE SPACE 21
6. INDEPENDENCE AND CONDITIONAL PROBABILITY (PRELIMINARY DISCUSSION) 22
7.
DEPENDENCE EXAMPLES 24
8. INFERIOR AND SUPERIOR LIMITS OF SEQUENCES OF MEASURABLE SETS 26
9.
MATHEMATICAL COUNTERPARTS OF COIN TOSSING 27
10.
SETWISE CONVERGENCE OF MEASURE SEQUENCES 30
11.
OUTER MEASURE 32
12.
OUTER MEASURES OF COUNTABLE SUBSETS OF R 33
13.
DISTANCE ON A SET ALGEBRA DEFINED BY A SUBADDITIVE SET FUNCTION 33
14.
THE PSEUDOMETRIC SPACE DEFINED BY AN OUTER MEASURE 34
15.
NONADDITIVE SET FUNCTIONS 36
IV. MEASURE SPACES
37
1.
COMPLETION OF A MEASURE SPACE
(5,
S,
X)
37
2.
GENERALIZATION OF LENGTH ON R 38
3.
A GENERAL EXTENSION PROBLEM 38
4.
EXTENSION OF A MEASURE DEFINED ON A SET ALGEBRA 40
5.
APPLICATION TO BOREL MEASURES 41
6. STRENGTHENING OF THEOREM 5 WHEN THE METRIC SPACE
S
IS COMPLETE
AND
SEPARABLE 41
7.
CONTINUITY PROPERTIES OF MONOTONE FUNCTIONS 42
8. THE CORRESPONDENCE BETWEEN MONOTONE INCREASING FUNCTIONS ON R
AND
MEASURES ON B(R) 43
9. DISCRETE AND CONTINUOUS DISTRIBUTIONS ON R 47
10.
LEBESGUE-STIELTJES MEASURES ON
R
N
AND THEIR CORRESPONDING
MONOTONE FUNCTIONS 47
11.
PRODUCT MEASURES 48
12.
EXAMPLES OF MEASURES ON R^ 49
13.
MARGINAL MEASURES 50
14.
COIN TOSSING 50
15.
THE CARATHE"ODORY MEASURABILITY CRITERION 51
16.
MEASURE HULLS 52
V. MEASURABLE FUNCTIONS
53
1.
FUNCTION MEASURABILITY 53
2.
FUNCTION MEASURABILITY PROPERTIES 56
3.
MEASURABILITY AND SEQUENTIAL CONVERGENCE 58
4.
BAIRE FUNCTIONS 58
5.
JOINT DISTRIBUTIONS 60
6. MEASURES ON FUNCTION (COORDINATE) SPACE 60
CONTENTS IX
7.
APPLICATIONS OF COORDINATE SPACE MEASURES 61
8. MUTUALLY INDEPENDENT RANDOM VARIABLES ON A PROBABILITY SPACE 63
9.
APPLICATION OF INDEPENDENCE: THE 0-1 LAW 64
10.
APPLICATIONS OF THE 0-1 LAW 64
11.
A PSEUDOMETRIC FOR REAL VALUED MEASURABLE FUNCTIONS ON A MEASURE
SPACE
65
12.
CONVERGENCE IN MEASURE 67
13.
CONVERGENCE IN MEASURE VS. ALMOST EVERYWHERE CONVERGENCE 68
14.
ALMOST EVERYWHERE CONVERGENCE VS. UNIFORM CONVERGENCE 69
15.
FUNCTION MEASURABILITY VS. CONTINUITY 69
16.
MEASURABLE FUNCTIONS AS APPROXIMATED BY CONTINUOUS FUNCTIONS 70
17.
ESSENTIAL SUPREMUM AND INFIMUM OF A MEASURABLE FUNCTION 71
18.
ESSENTIAL SUPREMUM AND INFIMUM OF A COLLECTION OF
MEASURABLE
FUNCTIONS 71
VI.
INTEGRATION
73
1.
THE INTEGRAL OF A POSITIVE STEP FUNCTION ON A MEASURE SPACE (5,S,
X)
73
2.
THE INTEGRAL OF A POSITIVE FUNCTION 74
3.
INTEGRATION TO THE LIMIT FOR MONOTONE INCREASING SEQUENCES
OF
POSITIVE FUNCTIONS 75
4.
FINAL DEFINITION OF THE INTEGRAL 76
5.
AN ELEMENTARY APPLICATION OF INTEGRATION 79
6. SET FUNCTIONS DEFINED BY INTEGRALS 80
7.
UNIFORM INTEGRABILITY TEST FUNCTIONS 81
8. INTEGRATION TO THE LIMIT FOR POSITIVE INTEGRANDS 82
9. THE DOMINATED CONVERGENCE THEOREM 83
10.
INTEGRATION OVER PRODUCT MEASURES 84
11.
JENSEN'S INEQUALITY 87
12.
CONJUGATE SPACES AND HOLDER'S INEQUALITY 88
13.
MINKOWSKI'S INEQUALITY 89
14.
THE
L
P
SPACES AS NORMED LINEAR SPACES 90
15.
APPROXIMATION OF
IF
FUNCTIONS 91
16.
UNIFORM INTEGRABILITY 94
17.
UNIFORM INTEGRABILITY IN TERMS OF UNIFORM INTEGRABILITY TEST FUNCTIONS
95
18.
L
1
CONVERGENCE AND UNIFORM INTEGRABILITY 95
19.
THE COORDINATE SPACE CONTEXT 96
20.
THE RIEMANN INTEGRAL 98
21.
MEASURE THEORY VS. PREMEASURE THEORY ANALYSIS 101
VII. HILBERT SPACE
103
1.
ANALYSIS OF L
2
103
2.
HILBERT SPACE 104
3.
THE DISTANCE FROM A SUBSPACE 106
4.
PROJECTIONS 107
5.
BOUNDED LINEAR FUNCTIONALS ON J) 108
X MEASURE THEORY
6. FOURIER SERIES 109
7.
FOURIER SERIES PROPERTIES 110
8. ORTHOGONALIZATION (ERHARDT SCHMIDT PROCEDURE) 111
9. FOURIER TRIGONOMETRIC SERIES 112
10.
TWO TRIGONOMETRIC INTEGRALS 113
11.
HEURISTIC APPROACH TO THE FOURIER TRANSFORM VIA FOURIER SERIES 113
12.
THE FOURIER-PLANCHEREL THEOREM 115
13.
ERGODIC THEOREMS 117
VIII. CONVERGENCE
OF
MEASURE SEQUENCES
123
1.
DEFINITION OF CONVERGENCE OF A MEASURE SEQUENCE 123
2.
LINEAR FUNCTIONALS ON SUBSETS OF C(S) 126
3.
GENERATION OF POSITIVE LINEAR FUNCTIONALS BY MEASURES
(5
COMPACT METRIC). 128
4.
C(S) CONVERGENCE OF SEQUENCES IN
M(S)
(S
COMPACT METRIC) 131
5.
METRIZATION OF M(S) TO MATCH C(S) CONVERGENCE; COMPACTNESS
OF
M
C
(S)
(5 COMPACT METRIC) 132
6. PROPERTIES OF THE FUNCTION U-|I
\F]
,
FROM
M(S),
IN THE D
M
METRIC
INTO
R (S COMPACT METRIC) 133
7.
GENERATION OF POSITIVE LINEAR FUNCTIONALS ON C
0
(5)
BY MEASURES
(S
A LOCALLY COMPACT BUT NOT COMPACT SEPARABLE METRIC SPACE) 135
8.
CO(5) AND
CQO(5)
CONVERGENCE OF SEQUENCES IN M(S) (S A LOCALLY
COMPACT
BUT NOT COMPACT SEPARABLE METRIC SPACE) 136
9. METRIZATION OF
M(S)
TO MATCH C
0
(S)
CONVERGENCE; COMPACTNESS
OF
M
C
(S)
(S A LOCALLY COMPACT BUT NOT COMPACT SEPARABLE METRIC
SPACE,
C A STRICTLY POSITIVE NUMBER) 137
10.
PROPERTIES OF THE FUNCTION
U-U[/],
FROM M(S) IN THE D
0M
METRIC
INTO
R (5 A LOCALLY COMPACT BUT NOT COMPACT SEPARABLE METRIC SPACE) 138
11.
STABLE C
0
(S)
CONVERGENCE OF SEQUENCES IN M
(S)
(5 A LOCALLY
COMPACT
BUT NOT COMPACT SEPARABLE METRIC SPACE) 139
12.
METRIZATION OF M(S) TO MATCH STABLE C
0
(S)
CONVERGENCE (S A LOCALLY
COMPACT
BUT NOT COMPACT SEPARABLE METRIC SPACE) 139
13.
PROPERTIES OF THE FUNCTION |A-YYFI!/L, FROM M(5) IN THE
D
M
'
METRIC INTO
R
(S A LOCALLY COMPACT BUT NOT COMPACT SEPARABLE METRIC SPACE) 141
14.
APPLICATION TO ANALYTIC AND HARMONIC FUNCTIONS 142
IX. SIGNED MEASURES
145
1.
RANGE OF VALUES OF A SIGNED MEASURE 145
2.
POSITIVE AND NEGATIVE COMPONENTS OF A SIGNED MEASURE 145
3.
LATTICE PROPERTY OF THE CLASS OF SIGNED MEASURES 146
4.
ABSOLUTE CONTINUITY AND SINGULARITY OF A SIGNED MEASURE 147
5.
DECOMPOSITION OF A SIGNED MEASURE RELATIVE TO A MEASURE 148
6.
A BASIC PREPARATORY RESULT ON SINGULARITY 150
7.
INTEGRAL REPRESENTATION OF AN ABSOLUTELY CONTINUOUS MEASURE 150
8.
BOUNDED LINEAR FUNCTIONALS ON L
1
151
CONTENTS XI
9. SEQUENCES OF SIGNED MEASURES 152
10.
VITALI-HAHN-SAKS THEOREM (CONTINUED) 155
11.
THEOREM 10 FOR SIGNED MEASURES 155
X. MEASURES AND FUNCTIONS OF BOUNDED VARIATION
ON
R 157
1.
INTRODUCTION 157
2.
COVERING LEMMA 157
3.
VITALI COVERING OF A SET 158
4.
DERIVATION OF LEBESGUE-STIELTJES MEASURES AND OF MONOTONE
FUNCTIONS
158
5.
FUNCTIONS OF BOUNDED VARIATION 160
6. FUNCTIONS OF BOUNDED VARIATION VS. SIGNED MEASURES 163
7.
ABSOLUTE CONTINUITY AND SINGULARITY OF A FUNCTION OF BOUNDED VARIATION
164
8.
THE CONVERGENCE SET OF A SEQUENCE OF MONOTONE FUNCTIONS 165
9.
HELLY'S COMPACTNESS THEOREM FOR SEQUENCES OF MONOTONE FUNCTIONS 165
10.
INTERVALS OF UNIFORM CONVERGENCE OF A CONVERGENT SEQUENCE OF
MONOTONE FUNCTIONS 166
11.
C(/) CONVERGENCE OF MEASURE SEQUENCES ON A COMPACT INTERVAL / 166
12.
C
0
(R)
CONVERGENCE OF A MEASURE SEQUENCE 167
13.
STABLE C
0
(R)
CONVERGENCE OF A MEASURE SEQUENCE 169
14.
THE CHARACTERISTIC FUNCTION OF A MEASURE 169
15.
STABLE C O(R) CONVERGENCE OF A SEQUENCE OF PROBABILITY DISTRIBUTIONS 171
16.
APPLICATION TO A STABLE C
0
(R)
METRIZATION OF M(R) 172
17.
GENERAL APPROACH TO DERIVATION 172
18.
A RATIO LIMIT LEMMA 174
19.
APPLICATION TO THE BOUNDARY LIMITS OF HARMONIC FUNCTIONS 176
XI.
CONDITIONAL EXPECTATIONS; MARTINGALE THEORY
179
1.
STOCHASTIC PROCESSES 179
2.
CONDITIONAL PROBABILITY AND EXPECTATION 179
3 CONDITIONAL EXPECTATION PROPERTIES 183
4.
FILTRATIONS AND ADAPTED FAMILIES OF FUNCTIONS 187
5.
MARTINGALE THEORY DEFINITIONS 188
6. MARTINGALE EXAMPLES 189
7.
ELEMENTARY PROPERTIES OF (SUB- SUPER-) MARTINGALES 190
8. OPTIONAL TIMES 191
9. OPTIONAL TIME PROPERTIES 192
10.
THE OPTIONAL SAMPLING THEOREM 193
11.
THE MAXIMAL SUBMARTINGALE INEQUALITY 194
12.
UPCROSSINGS AND CONVERGENCE 194
13.
THE SUBMARTINGALE UPCROSSING INEQUALITY 195
14.
FORWARD (SUB- SUPER-) MARTINGALE CONVERGENCE 195
15.
BACKWARD MARTINGALE CONVERGENCE 197
16.
BACKWARD SUPERMARTINGALE CONVERGENCE 198
XII MEASURE THEORY
17.
APPLICATION OF MARTINGALE THEORY TO DERIVATION 199
18.
APPLICATION OF MARTINGALE THEORY TO THE 0-1 LAW 201
19.
APPLICATION OF MARTINGALE THEORY TO THE STRONG LAW OF LARGE NUMBERS 201
20.
APPLICATION OF MARTINGALE THEORY TO THE CONVERGENCE OF INFINITE SERIES
202
21.
APPLICATION OF MARTINGALE THEORY TO THE BOUNDARY LIMITS OF
HARMONIC
FUNCTIONS 203
NOTATION
205
INDEX
207 |
| any_adam_object | 1 |
| author | Doob, Joseph L. 1910-2004 |
| author_GND | (DE-588)12778022X |
| author_facet | Doob, Joseph L. 1910-2004 |
| author_role | aut |
| author_sort | Doob, Joseph L. 1910-2004 |
| author_variant | j l d jl jld |
| building | Verbundindex |
| bvnumber | BV008879684 |
| callnumber-first | Q - Science |
| callnumber-label | QA325 |
| callnumber-raw | QA325.D66 1994 |
| callnumber-search | QA325.D66 1994 |
| callnumber-sort | QA 3325 D66 41994 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| classification_tum | MAT 280f |
| ctrlnum | (OCoLC)320301876 (DE-599)BVBBV008879684 |
| dewey-full | 515/.4220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.42 20 |
| dewey-search | 515/.42 20 |
| dewey-sort | 3515 242 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV008879684</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20000518</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">940209s1994 xxu |||| 00||| engod</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">940397005</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387940553</subfield><subfield code="9">0-387-94055-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540940553</subfield><subfield code="9">3-540-94055-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)320301876</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV008879684</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA325.D66 1994</subfield></datafield><datafield tag="080" ind1=" " ind2=" "><subfield code="a">519.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.42 20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 430</subfield><subfield code="0">(DE-625)143239:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">28-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 280f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60Bxx</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">60A10</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Doob, Joseph L.</subfield><subfield code="d">1910-2004</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)12778022X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Measure theory</subfield><subfield code="c">J. L. Doob</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 210 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">143</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Measure theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probabilities</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Maßtheorie</subfield><subfield code="0">(DE-588)4074626-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">143</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">143</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005873364&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-005873364</subfield></datafield></record></collection> |
| id | DE-604.BV008879684 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-07T13:03:11Z |
| institution | BVB |
| isbn | 0387940553 3540940553 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005873364 |
| oclc_num | 320301876 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-12 DE-19 DE-BY-UBM DE-824 DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-20 DE-521 DE-634 DE-83 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-12 DE-19 DE-BY-UBM DE-824 DE-29T DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-20 DE-521 DE-634 DE-83 DE-188 |
| physical | XII, 210 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Doob, Joseph L. 1910-2004 Verfasser (DE-588)12778022X aut Measure theory J. L. Doob New York [u.a.] Springer 1994 XII, 210 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 143 Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Graduate texts in mathematics 143 (DE-604)BV000000067 143 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005873364&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Doob, Joseph L. 1910-2004 Measure theory Graduate texts in mathematics Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Measure theory |
| title_auth | Measure theory |
| title_exact_search | Measure theory |
| title_full | Measure theory J. L. Doob |
| title_fullStr | Measure theory J. L. Doob |
| title_full_unstemmed | Measure theory J. L. Doob |
| title_short | Measure theory |
| title_sort | measure theory |
| topic | Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Measure theory Probabilities Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005873364&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT doobjosephl measuretheory |