Introduction to Probability and Measure

Contents: Preface. 1. Probability on Boolean algebras. 2. Extension of measures. 3. Borel maps. 4. Integration. 5. Measures on product spaces. 6. Hilbert space and conditional expectation. 7. Weak convergence of probability measures. 8. Invariant measures on groups.

"According to a remark attributed to Mark Kac, probability theory is Measure theory with a Soul. Furthermore, measure theory has its own ramifications in topics like function spaces, operator theory, generalized functions, ergodic theory, group representations, quantum probability etc. On the other hand recent explosive developments in the applications of probability theory have imposed the need for a good grasp of measure theory among a wide spectrum of scholars ranging from economists to engineers and physicists to psychologists. This book with its choice of proofs, remarks, examples and exercises has been prepared taking both these aesthetic and practical aspects into account."