Duality in Measure Theory
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796 Corneliu Constantinescu
Duality in Measure Theory
Springer-Verlag Berlin Heidelberg New York 1980
Author
Corneliu Constantinescu Mathematisches Seminar ETH-Zentrum 8092 ZLJrich Switzerland
AMS Subject Classifications (1980): Primary: 28A33, 28B05, 46E27, 46G10 Secondary: 28A10, 28A25, 28A35, 28C05, 46A20, 46A32, 4 6 A 4 0 ISBN 3-540-09989-1 ISBN 0-387-09989-1
Springer-Verlag Berlin Heidelberg NewYork Springer-Verlag NewYork Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Table
of Contents Page
Introduction
.....................................................
1
~ I. P r e l i m i n a r i e s i. V e c t o r
lattices
2. M e a s u r e s
..........................................
5
..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3. I n t e g r a t i o n 4. C o n c a s s a @ e 5. S o m e
..............................................
7
...............................................
i0
notations
6. H y p e r s t o n i a n
i.
Bounded
...........................................
spaces
......................................
representations
of
(X,M)
24
..............................
26
.................................
31
of measures
3. R e p r e s e n t a t i o n s
of
4.
Supplementar [ results
~ 3. D u a l s
of spaces
!. S t r u c t u r e s 2. S p a c e s 3. T h e
4. S t r u c t u r e s 5. s p a c e s 6. T h e
7. T e n s o r
on
Mp
the
representations
.....
38
........................................
45
to a measure
..........................
53
...............................
59
...............................
64
.....................................
82
Mb_
• ...............................
89
of m e a s u r e s
91
M~ Mb, on
M
and Mc_ and
of o p e r a t o r s
spaces
concernin~
of measures
associated
spaces
16
.........................
2. R e p r e s e n t a t i o n s
(xtM)
12
Mb
products
and Qf
M~ c-
spaces
8. T h e
strong
D.-P.vpropert~
9. T h e
strong
approximation
...................
...............................
105
property .........................
108
~=~&=~tor
measures
i.
Preliminaries
2.
The
3.
Operators
4.
Vector
5.
Topologies
Bibliography Index
integral
........................................... with
on
subspaces
measures on
respect
on the
to
of
M~ c--
Hausdorff spaces
a vector
of
measure
...........
.........................
spaces vector
........
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