Measures on Topological Semigroups: Convolution Products and Random Walks
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547 Arunava Mukherjea Nicolas A.Tserpes Measures on
Topological Semigroups: Convolution Products and Random Walks
Springer-Verlag Berlin.Heidelberg 9New York 1976
Authors
Prof. Arunava Mukherjea Prof. Nicolas A. T s e r p e s University of South Florida Department of Mathematics Tampa, Florida 3 3 6 2 0 / U S A
AMS Subject Classifications (1970): 43A05, 60G50, 60.115 ISBN 3-540-07987-4 Springer-Verlag Berlin 9 Heidelberg 9 New York ISBN 0-38?-0?987-4 Springer-Verlag New York 9 Heidelberg 9 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 w 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 9 Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.
Preface This monograph
is an outgrowth
of the lecture notes of a
series of lectures given by the first author Statistical supplement
Institute
material
during the fall of 1973.
in many ways the material
"Probabilities
on Algebraic
that appears
Processes:
much to these two mathematicians.
of colloquium
in the book
by Ulf Grenander
Behavior"
who have worked
a number of stimulating
These notes
and the
IV and V of the book "Markov
and Asymptotic
Like most mathematicians
group Symposium
presented
Structures"
in Chapters
Structure
when he was invited
in the Indian
by M. Rosenblatt.
in this area, we owe
We also gratefully
conversations
acknowledge
with Prof. M. Rosenblatt
to speak in the Wayne
State University
Semi-
in 1968 and when he was invited to give a series
talks at the University
of South Florida
in early
1973. Our primary objective reader with a brief, of probability
but somewhat
of probability
topological
measures
values
of products
of one-sided
probability Hausdorff
measure
completely
and
iterates
semigroups,
random variables
semigroup
of
on locally
(iii) almost
and
sure taking
(iv) the recurrence
random walks induced by a
on a compact Hausdorff simple topological
interesting
or locally compact
semigroup.
of probability
while leaving out many other
in the
(ii) the limit behavior
matrices
and two-sided
cover only certain aspects
measures
topological
of independent simple
semigroups
sequence of convolution
of stochastic
in a completely
behavior
account of the theory
probability
on different
the
(i) the characterization
semigroups
and unaveraged
also on semigroups convergence
problems:
and r*-invariant
compact Hausdorff of the averaged
complete
and measure on topological
context of the following the idempotent
in these notes is to provide
Thus our notes
theory on semigroups aspects
such as the study
IV of infinitely d
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