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. 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