Download A1982PN64900001

.
This Week’s Citation Classic________
Parihasarathy K K. Probability measures on metric spaces.
New York: Academic Press, 1967. 2’76p.
tDept. Pi’obability and Statistics, Univ. Sheffield, Sheffield, EnglandJ
12
The structure of 8o~eisets In complete and. •HUbert space. - This led tonew notions like
separable metric spaces, con~duth,nof shift compactness, Gaussian distribution on
probability measwes in groups and Hubert a group, and finalIy~L&vy-I(hinchine represpaces, andgenerAlisations of classical limit
sentations in the new setting. The Levytheorems for sums of independent random
Ithinchine representation in a Hilbert space4
variables in such spaces are investigated.
is also called the Varadhan representation.
fThe Science Citation Index’> (SCI®) and the
“1 spent the year 1962-1963 in Moscow
Social Sciences Citation Index’> (SSCI’>) jp,.
dicate that this book has been cited in over
and found that many of our results were be450 publications since 1967.]
ing rediscovered. Hence, i gave a few seminars and determined in my mind to put
down these results in book form. In colLaboration with V.V. Sazonov, I made some
I(,R. Paithasarathy
minor improvements
Indsan Statistical Institute
5 in -the theory developed at Calcutta. In November 1963, 1
Delhi Centre
returned to Calcutta but, owing to the influNew Delhi 110016
ence of the US on Varadarajan, oi.sr research
India
work took an entirely different 8irection.
August 21, 1982 Owing to marriage and the difficulties of
daily life in Calcutta, all the members of this
“In 1956, V.5. Varadarajan and I toined quartet emigrated to the West. I landed in
the Indian Statistical Institute at Calcutta Sheffield ini%5 and found that the atmoand came into contact with R. Ranga Rao. A sphere under the leadership of j. Gani was
few years later another young probabilist, very pleasant and at the same time competiS,R.S. Varadhan, joined our group. Calcutta tive. To make my mark I organised a semiwas a difficult city and the bamboo sheds in nar onthe Calcutta results and summarised
which we lived did not make life easier. them in my notes. The Amei’icanpmbabthst
However, the institute had a good library F. Lukacs visited the department and in the
and international contacts. We forgot all course of a chatproposed that the notes be
the misery of life by plunging into mathe- published in book form. With very little
matical ;esearch.U Soon we became change the book was published in 1967.
familiar with the entire spectrum of work Soon after that, 1 was rewarded with a perdone by the Russian school of probabilists sonal chair at the University of Manchester.
under the leadership of AN. Kolmogorov.
“This book has been cited for several
Varadarajan had already rediscovered many reasons. The first chapter of the book which
results of Yu.V. Prohorov on the interplay was written only in order to include some
between topology and measure and taught technical points assumed, rather .strangel~’,
us about this topic. Later he left for Prince- a special importance in-mathematical ecoton in order to pursue his research in a dif- nomics and other social sciences. Probably
ferent direction and the remaining three of for the first time a summary of the wellus embarked on a project under the leader- known work of the Polish school on Borel
ship of Ranga Rao to generalise systemati- and analytic sets appeared here in an easily
cally the contents of the famous book on comprehensible form and made the book
limit theorems
by Kolmogorov and By. popular among nonprobabilists. For a more
3
Gnedenko to ‘sums’ of independent ran- recent review see Probability
6 Measures on
dom variables with values in a group or Locally Compact Groups.”
1. ~
--~yKR, i.~gaR.oR& Vasa~ Si S. Os the calegory ol indeconiposable distributions on
topologicalgroups. Tssns. Asser. Math. Soc. *12:200-17, 1962.
2.
. Pzo~Qh~
diitiibu*iom on Lwih, ,,,.,o.~
111. 1. Math. 733749. 1963.
3. Gaeás.L. 1 V. £ ~j~oe
A N.lash diwthtaioiufor ~z 4~—~p’sdiso
sa~i,a.sa~6lzs.
Reading, England: Addison-Wesley, 1954. 264 p.
4. Vae.d~iaS iS. Lthslt theorems toe ~
~ àdegesthnt ~a4em s’aslabka .4th aslue. in .1*ilbc~~.
Saak*ya 24:213-38,1962.
5. f.s~re*y K ii Ssros., V V. On the representation of infinitely disisible dittributions on locally compact
Abelian groups. Theor. Probab. Appi—Eng!. Tr. 5:118-22, 1964.
3
6. Ba~.rH. ~ubabhi~
ta~
00 ~oorE, cvsNpactgre~s. B
~
i9i~.S lp.
14
Pc&~
Q~RENT~NThTS~
~
I
I