The authors believe that a proper treatment of probability theory
requires an adequate background in the theory of finite measures in
general spaces. The first part of their book sets out this material
in a form that not only provides an introduction for intending
specialists in measure theory but also meets the needs of students
of probability. The theory of measure and integration is presented
for general spaces, with Lebesgue measure and the Lebesgue integral
considered as important examples whose special properties are
obtained. The introduction to functional analysis which follows
covers the material (such as the various notions of convergence)
which is relevant to probability theory and also the basic theory
of L2-spaces, important in modern physics. The second part of the
book is an account of the fundamental theoretical ideas which
underlie the applications of probability in statistics and
elsewhere, developed from the results obtained in the first part. A
large number of examples is included; these form an essential part
of the development.
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