This book is a modern introduction to measure theoretic
probability and statistical inference well targeted for
graduate students in econometrics at top institutions.
It would make an excellent textbook for first year graduate
students who intend to specialize in econometrics or who
have an advanced mathematical background, and it would
also be a useful part of any graduate econometrics course.
It is concise and intensely focused on the key conceptual
points, thus counteracting the tendency toward long-windedness
apparent in some recent econometric texts. Nevertheless,
it provides many valuable insights into difficult material.
In particular, the discussions of sigma fields and conditional
expectation given a sigma field are very helpful. The coverage
of multivariate concepts alongside univariate ones is particularly
useful to econometricians and something that is missing
from most comparable statistical texts. The author has
a mature attitude to proof, providing complete and illuminating
proofs of some results but making liberal use of simplifications
provided by special cases, for example in Theorems 4.1
and 4.5 and Section 5.2.2, to shorten and focus the arguments.
The proofs themselves are very clear and well presented.
Carefully chosen diagrams are given throughout the book
that nicely illustrate many of the key concepts. In addition,
each chapter contains a long list of problems of varying
complexity, which will be useful to instructors.