Gaussian Measures in Banach Spaces
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463 Hui-Hsiung Kuo
Gaussian Measures
in Banach Spaces
Springer-Verlag Berlin. Heidelberg- New York 1975
Author Prof. Hui-Hsiung Kuo University of Virginia Department of Mathematics Charlottesville, VA 22903 USA
Library of Ceagress Cataloging in Publication Data
Kuo, H ~ - H s i ~ ,
1941-
Gaussian measures in Banach spaces.
(~ecture notes in m~them~ties ; v. 463) Bibliography: p. Includes in&ex. i. C~ussian measures. 2. Banach spaces. I. Title. II. Series: Lecture notes in mathematics (Berlin) ;
v. 463. QA3.IR8
no. ~63 [QA312]
510'.8s [515'.42]
75-16345
AMS Subject Classifications (1970): 2 8 A 4 0 ISBN 3-540-07173-3 Springer-Verlag Berlin. Heidelberg" N e w Y o r k ISBN 0-387-07173-3 Springer-Verlag New Y o r k . Heidelberg Berlin 9 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 s 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. 9 by Springer-Verlag Berlin Heidelberg 9 1975 Printed in Germany Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
PREFACE
This m o n o g r a p h entitled
is b a s e d on the lecture
"Applications
of M e a s u r e
Theory"
1974 at the U n i v e r s i t y
of Virginia.
the m a t e r i a l
does
very well.
delivered Our p r i m a r y
introduction
to the n o t i o n
of the r e l a t e d first three added
topics.
sections
in w h e n
We c o v e r e d
I rewrote
K.D.
Elworthy
on Banach manifolds. include
their w o r k s
I would Gross
and m a t h e m a t i c a l
that
Kiyosi
two c h a p t e r s
in d e t a i l s among
it w o u l d
an some
and the
sections
were
regret
that
the r e c e n t w o r k s others
see,
title
and study
I deeply
of
on the i n t e g r a t i o n
be too a m b i t i o u s
my a p p r e c i a t i o n
parts
The c o n v e r s a t i o n s I would
to
preparation
of these notes
Kuo for typing is p a r t i a l l y
with
them have
M y special
always
Trent
thanks
the m a n u s c r i p t .
supported
Leonard
encouragement
like to thank T a v a n
of the manuscript.
Smith and F u k u k o
to P r o f e s s o r
Ito for their c o n s t a n t
influence.
to Barbara
Science
space
of
in these notes.
been a source of inspiration. for p r o o f - r e a d i n g
can e a s i l y
the c o u r s e ' s
last four
notes.
and R. Ramer,
like to express
and P r o f e s s o r
the first
the lecture
I feel
with
Wiener
III. The
in this c o u r s e we did not d i s c u s s J. Eells,
in the S p r i n g
in this course was to give
of a b s t r a c t
of C h a p t e r
given
As the reader
not c o o p e r a t e
object
notes of a course
go
The
by the N a t i o n a l
Foundation. H. -H.
Kuo
TABLE
Chapter
I.
Gaussian
measures
w
Hilbert-Schmidt
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