PREFACE
J
.L. DOOB
My first contact with Doeblin was a letter from him, protesting (justifi-
ably) that I should have written him about a slip in his 1938 paper instead
of simply noting the lapse in a later paper of my own. I was making so
many errors in my own work, that the error in Doeblin 's paper seemed
no big deal to me! To do him justice, Doeblin held no grudge about my
reference and sent me a card showing how to fix his proof. Thereafter, we
exchanged reprints and letters; in particular he sent me his thesis. This
thesis was published in 1937 in a rather inaccessible journal, and I thought
so highly of it that I printed some of its results, with few changes, in my
book sl "Stochastic Processes" in 1953. When the news spread that I had
a copy of the thesis, I received so many requests for it in those pre Xerox
days that I finally had it microfilmed to facilitate distribution.
In the late thirties, probability theory was in the process of modernization
and was gradually being incorporated into the body of standard mathe-
matics. Deep researchers like Doeblin delayed the acceptance of probabil-
ity as mathematics by their virtuosity in dealing not only with probabil-
ities, but also with the subtleties of sample functions. The latter seemed
alien to classical analysts who while experiencing no difficulty in accept-
ing analytical studies of conditional probabilities which led to difference
equations, partial differential equations, and integral equations, in which
the probabilistic background was hardly hinted at, found sample function
contexts incomprehensible and therefore considered them outside mathe-
matics.
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