A Course In Probability Theory - Chung K L
In this new edition, I have added a Supplement on Measure and Integral.
The subject matter is first treated in a general setting pertinent to an abstract
measure space, and then specified in the classic Borel-Lebesgue case for the
real line. The latter material, an essential part of real analysis, is presupposed
in the original edition published in 1968 and revised in the second edition
of 1974. When I taught the course under the title "Advanced Probability"
at Stanford University beginning in 1962, students from the departments of
statistics, operations research (formerly industrial engineering), electrical engi-
engineering, etc. often had to take a prerequisite course given by other instructors
before they enlisted in my course. In later years I prepared a set of notes,
lithographed and distributed in the class, to meet the need. This forms the
basis of the present Supplement. It is hoped that the result may as well serve
in an introductory mode, perhaps also independently for a short course in the
stated topics.
The presentation is largely self-contained with only a few particular refer-
references to the main text. For instance, after (the old) §2.1 where the basic notions
of set theory are explained, the reader can proceed to the first two sections of
the Supplement for a full treatment of the construction and completion of a
general measure; the next two sections contain a full treatment of the mathe-
mathematical expectation as an integral, of which the properties are recapitulated in
§3.2. In the final section, application of the new integral to the older Riemann
integral in calculus is described and illustrated with some famous examples.
Throughout the exposition, a few side remarks, pedagogic, historical, even judgmental, of the kind I used to drop in the classroom, are approximately
reproduced.
In drafting the Supplement, I consulted Patrick Fitzsimmons on several
occasions for support. Giorgio Letta and Bernard Bru gave me encouragement
for the uncommon approach to Borel's lemma in §3, for which the usual proof
always left me disconsolate as being too devious for the novice's appreciation.
A small number of additional remarks and exercises have been added to
the main text.Warm thanks are due: to Vanessa Gerhard of Academic Press who deci-
deciphered my handwritten manuscript with great ease and care; to Isolde Field
of the Mathematics Department for unfailing assistence; to Jim Luce for a
mission accomplished. Last and evidently not least, my wife and my daughter
Corinna performed numerous tasks indispensable to the undertaking of this
publication.
- Modern Cryptography: A Course In Probability Theory by Chung K L
- Publisher: ACADEMIC PRESS A 1-iorcourt Science and Technology Company
- Pub Date: Copyright © 2001, 1974, 1968 by Academic Press
- ISBN: 0-12-174151-6
- Pages:432
In this new edition, I have added a Supplement on Measure and Integral.
The subject matter is first treated in a general setting pertinent to an abstract
measure space, and then specified in the classic Borel-Lebesgue case for the
real line. The latter material, an essential part of real analysis, is presupposed
in the original edition published in 1968 and revised in the second edition
of 1974. When I taught the course under the title "Advanced Probability"
at Stanford University beginning in 1962, students from the departments of
statistics, operations research (formerly industrial engineering), electrical engi-
engineering, etc. often had to take a prerequisite course given by other instructors
before they enlisted in my course. In later years I prepared a set of notes,
lithographed and distributed in the class, to meet the need. This forms the
basis of the present Supplement. It is hoped that the result may as well serve
in an introductory mode, perhaps also independently for a short course in the
stated topics.
The presentation is largely self-contained with only a few particular refer-
references to the main text. For instance, after (the old) §2.1 where the basic notions
of set theory are explained, the reader can proceed to the first two sections of
the Supplement for a full treatment of the construction and completion of a
general measure; the next two sections contain a full treatment of the mathe-
mathematical expectation as an integral, of which the properties are recapitulated in
§3.2. In the final section, application of the new integral to the older Riemann
integral in calculus is described and illustrated with some famous examples.
Throughout the exposition, a few side remarks, pedagogic, historical, even judgmental, of the kind I used to drop in the classroom, are approximately
reproduced.
In drafting the Supplement, I consulted Patrick Fitzsimmons on several
occasions for support. Giorgio Letta and Bernard Bru gave me encouragement
for the uncommon approach to Borel's lemma in §3, for which the usual proof
always left me disconsolate as being too devious for the novice's appreciation.
A small number of additional remarks and exercises have been added to
the main text.Warm thanks are due: to Vanessa Gerhard of Academic Press who deci-
deciphered my handwritten manuscript with great ease and care; to Isolde Field
of the Mathematics Department for unfailing assistence; to Jim Luce for a
mission accomplished. Last and evidently not least, my wife and my daughter
Corinna performed numerous tasks indispensable to the undertaking of this
publication.
