Background
Tulcea, Cassius Ionescu was born on October 14, 1923 in Bucharest, Rumania. Son of Ioan and Ana (Caselli) Ionescu Tulcea. naturalized, 1967.
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(The problem as to whether or not there exists a lifting o...)
The problem as to whether or not there exists a lifting of the M't/. 1 space ) corresponding to the real line and Lebesgue measure on it was first raised by A. Haar. It was solved in a paper published in 1931 102 by 1. von Neumann, who established the existence of a lifting in this case. In subsequent papers J. von Neumann and M. H. Stone 105, and later on 1. Dieudonne 22, discussed various algebraic aspects and generalizations of the problem. Attemps to solve the problem as to whether or not there exists a lifting for an arbitrary M't/. space were unsuccessful for a long time, although the problem had significant connections with other branches of mathematics. Finally, in a paper published in 1958 88, D. Maharam established, by a delicate argument, that a lifting of M't/. always exists (for an arbi trary space of a-finite mass). D. Maharam proved first the existence of a lifting of the M't/. space corresponding to a product X = TI {ai,b,} ieI and a product measure J.1= Q9 J.1i' with J.1i{a;}=J.1i{b,}=! for all iE/. ,eI Then, she reduced the general case to this one, via an isomorphism theorem concerning homogeneous measure algebras 87, 88. A different and more direct proof of the existence of a lifting was subsequently given by the authors in 65' A variant of this proof is presented in chapter 4.
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educator research mathematician
Tulcea, Cassius Ionescu was born on October 14, 1923 in Bucharest, Rumania. Son of Ioan and Ana (Caselli) Ionescu Tulcea. naturalized, 1967.
Master of Sciences, University Bucarest, 1946; Doctor of Philosophy, Yale, 1959.
Member faculty, U. Bucarest, 1946-1957; associate professor, U. Bucarest, 1952-1957; research associate, Yale University, 1957-1959; visiting lecturer, Yale University, 1959-1961; associate professor, University of Pennsylvania, 1961-1964; professor, University of Illinois, Urbana, 1964-1966; professor, Northwestern University, Evanston, Illinois, 1966-1990; professor emeritus, Northwestern University, Evanston, Illinois, since 1990.
(The problem as to whether or not there exists a lifting o...)
