**Almost Everywhere
Convergence: The Case
for the Ergodic Viewpoint**

### San Francisco, California 1991

**ALEXANDRA BELLOW** was born in Bucharest, Romania. Both of her parents were physicians; her mother was also a dedicated educator who enjoyed finding new ways of teaching arithmetic to children. "I was one of her first guinea pigs," says Bellow, "and that was a lot of fun."

In her last years in high school, Bellow had an inspiring mathematics teacher. "She was small, wiry, passionate about mathematics, and she knew no fear," Bellow recalls. "She was one of the few people I came across, as I grew up in communist Romania, who was not afraid of political repercussions. This was most remarkable in those days of fierce Stalinist repression." At that time, Bellow became increasingly aware that mathematics was one of the few disciplines that could enjoy relative freedom under a dictatorship.

She graduated from the University of Bucharest in 1957 with the equivalent of an MA degree. In the fall of that year, she came to the United States accompanying her first husband, the mathematician C. Ionescu Tulcea, who had been invited to participate in a special year in functional analysis at Yale University. She entered graduate school at Yale and received her PhD in 1959. While there, she came under the influence of Shizuo Kakutani, one of the founding fathers of Ergodic theory. "I have been under the Ergodic spell ever since," she remarks.

Her professional career took her to the University of Pennsylvania, the University of Illinois at Urbana-Champaign, and finally to Northwestern University, where she became a full professor in 1968. She has also greatly benefited from spending time at other institutions, such as the University of Minnesota, the Massachusetts Institute of Technology, Brandeis University, Gottingen University, the Hebrew University of Jerusalem, Tel-Aviv University, the California Institute of Technology, and the University of California at Los Angeles. While at Caltech, she held a Fairchild Distinguished Scholarship, and in 1987, she received a Humboldt Award from the Federal Republic of Germany, which she used primarily to spend time at Gottingen. Her professional activities include serving on the editorial boards of *The Transactions of the American Mathematical Society*, the *Annals of Probability*, and *Advances in Mathematics*.

It was during her tenure as a visiting professor at MIT that she met her present husband, the mathematician Alberto P. Calderon; the two shared an office. "Given the trials and ironies of my past," she reflects, "I find it astonishing that life can offer peace and happiness after fifty, and that mathematics has become an asset in the human aspects of my personal life:"

For a number of years, her mathematical interests centered on measure theory and, specifically, on problems connected with the notion of lifting of an L infinity space and applications of that concept. "The problem of almost everywhere convergence has always been close to my heart, and I returned to it time and again," she notes. In her Noether Lecture, Bellow chose to illustrate the Ergodic point of view with several problems of almost everywhere convergence, such as moving averages, Riemann sums, and so on. "I find these problems particularly appealing because they are at the crossroads of Ergodic theory, harmonic analysis, and number theory, and one can see the interplay among these fields at work."