Probability in Banach Spaces - ISBN:3540077936

Probability in Banach Spaces

Date: 12 April 2011, 15:14

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Probability in Banach Spaces is almost a quarter century old as a subject of study. It originated in 1953 in the thesis of Dr. Edith wurier, who proved the first Strong Law of Large Numbers for random variables taking values in a Banach space. Early work seemed largely to parallel the corresponding theorems for real and complex valued random variables, and for that reason did not attract much attention. Beginning in the early sixties, however, there began to develop a body of material tying the truth or falsity of probabilistic theorems in Banach spaces to the geometry of the spaces. Increasingly, the theorems seemed to indicate that our familiar theorems of probability were in fact probability-geometry theorems, where the accidental geometry of the real and complex numbers played an important part. Reducing the geometric hypotheses required the tightening of the probabilistic ones. The search for probability theorems has lead us into consideration of new classes of Banach spaces, and the dissection of the theorems in Banach spaces has led us into new probabilistic conditions. The Conference on Probability in Banach Spaces held at Oberwolfach in July, 1975, brought together for the first time many of those working in this newly burgeoning field. The comparison of results was widespread and fruitful, and this volume now brings these results to the mathematical public generally. We, the participants, invite all mathematicians to join US in this young and exciting field of study.

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