Preface
Say what you know, do what you must, come what may.
-Sofya Kovalevskay a
To us probability is the very guide of life.
-Bishop Josep h Butle r
A few years ago the University of Utah switche d fro m th e quarter syste m
to the semester system . Thi s change gave the facult y a chance to re-evaluat e
their cours e offerings . A s par t o f thi s re-evaluatio n proces s w e decide d t o
replace th e usua l year-lon g graduat e cours e i n probabilit y theor y wit h on e
that wa s a semeste r long . Ther e wa s goo d reaso n t o d o so . Th e rol e o f
probability i n mathematics , science , an d engineerin g was , an d stil l is , o n
the rise . Ther e i s increasin g deman d fo r a graduat e cours e i n probability .
And ye t th e typica l graduat e studen t i s no t abl e t o tackl e a larg e numbe r
of year-lon g course s outsid e hi s o r he r ow n researc h area . Thus , w e wer e
presented wit h a non-trivial challenge : Ca n w e offer a course that addresse s
the need s o f ou r own , a s wel l a s other , graduat e students , al l withi n th e
temporal confines of one semester? I believe that th e answer to the precedin g
question i s "yes. "
This book presents a cohesive graduate course in measure-theoretic prob -
ability tha t specificall y ha s th e one-semeste r studen t i n mind . Ther e is , i n
fact, ampl e material to cover an ordinary year-long course at a more leisurel y
pace. See , fo r example , th e man y section s tha t ar e entitle d complements ,
and thos e tha t ar e calle d applications . However , th e primar y goal s o f thi s
book ar e t o maintai n brevit y an d conciseness , an d t o introduc e probabilit y
quickly an d a t a modestl y dee p level . I hav e use d a s m y mode l a stan -
dard one-semeste r undergraduate cours e i n probability . I n tha t setting , th e
XI
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