Integration II: Chapters 7–9

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Springer Science & Business Media, Sep 7, 2004 - Mathematics - 326 pages
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Integration is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and  Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

The first volume of the English translation comprises Chapters 1-6; the present volume completes the translation with the remaining Chapters 7-9.

Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chapters 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).

 

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Contents

I
vii
II
xi
III
xv
IV
xviii
V
xix
VI
xx
VII
xxiii
VIII
xxiv
LXIII
61
LXIV
65
LXV
73
LXVI
75
LXVII
81
LXVIII
IG-1
LXIX
IG-3
LXX
IG-6

IX
xxv
X
xxvi
XI
xxx
XII
xxxii
XIII
xxxiv
XIV
xxxvii
XV
xli
XVI
xliii
XVII
xlviii
XVIII
xlix
XIX
l
XX
liii
XXI
lv
XXII
lviii
XXIII
lx
XXIV
lxv
XXVI
lxvi
XXVII
lxvii
XXVIII
lxviii
XXIX
lxxix
XXX
ii
XXXI
iv
XXXII
vi
XXXIII
vi
XXXIV
viii
XXXV
3
XXXVI
6
XXXVIII
7
XXXIX
8
XL
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XLI
11
XLII
12
XLIII
13
XLIV
15
XLV
16
XLVI
18
XLVII
21
XLVIII
22
XLIX
24
L
28
LI
34
LII
37
LIII
38
LIV
42
LV
44
LVI
46
LVII
48
LVIII
51
LIX
53
LX
55
LXI
56
LXII
59
LXXI
IG-8
LXXII
IG-9
LXXIII
IG-11
LXXIV
IG-12
LXXV
IG-13
LXXVI
IG-17
LXXVII
IG-20
LXXVIII
IG-22
LXXX
IG-24
LXXXI
IG-26
LXXXII
IG-29
LXXXIII
IG-31
LXXXIV
IG-33
LXXXV
IG-37
LXXXVI
IG-41
LXXXVIII
IG-44
LXXXIX
IG-46
XC
IG-49
XCI
IG-50
XCIII
IG-54
XCIV
IG-56
XCVI
IG-59
XCVII
IG-60
XCVIII
IG-63
XCIX
IG-64
C
IG-67
CI
IG-68
CII
IG-72
CIV
IG-74
CV
IG-75
CVI
IG-77
CVII
IG-78
CVIII
IG-82
CIX
IG-85
CX
6
CXI
7
CXII
10
CXIII
11
CXIV
99
CXV
102
CXVI
104
CXVII
106
CXVIII
108
CXX
112
CXXI
113
CXXII
117
CXXIII
118
CXXIV
120
CXXV
309
CXXVI
311
CXXVII
320
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Page 131 - DE LA VALLÉE POUSSIN. Intégrales de Lebesgue, fonctions d'ensembles, classes de Baire.

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About the author (2004)

Nicolas Bourbaki is the pseudonym for a group of mathematicians that included Henri Cartan, Claude Chevalley, Jean Dieudonne, and Andres Weil. Mostly French, they emphasized an axiomatic and abstract treatment on all aspects of modern mathematics in Elements de mathematique. The first volume of Elements appeared in 1939. Subsequently, a wide variety of topics have been covered, including works on set theory, algebra, general topology, functions of a real variable, topological vector spaces, and integration. One of the goals of the Bourbaki series is to make the logical structure of mathematical concepts as transparent and intelligible as possible. The books listed below are typical of volumes written in the Bourbaki spirit and now available in English.

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