Measure Theory for Analysis and Probability

Alok Goswami is Visiting Professor in the School of Mathematical and Computational Science at the Indian Association for the Cultivation of Science, Kolkata, West Bengal India. Earlier, he was a faculty member in the Theoretical Statistics and Mathematics Unit at the Indian Statistical Institute, West Bengal, Kolkata, India, for nearly 30 years, until his retirement in 2019, as Professor. He received his M.Stat. degree from the Indian Statistical Institute in 1980 and his Ph.D. degree from the Department of Mathematics in the University of Illinois at Urbana-Champaign, U.S.A., in 1986. He visited many other premier universities and institutes of India and abroad and is widely regarded as one of the top academicians in the field of probability theory. His primary research interests are probability and stochastic processes, while he has also done some collaborative research in statistics. B.V. Rao has been at Chennai Mathematical Institute, Tamil Nadu, India, since 2009, and is currently a Visiting Faculty there. Earlier, he served as a faculty member at the Indian Statistical Institute, Kolkata, for more than 30 years, before retiring as a Distinguished Professor in 2009. He received his M.Sc. in Statistics from Osmania University, Hyderabad, India, in 1965, and his Ph.D. from the Indian Statistical Institute, Kolkata, in 1970. His research interests include descriptive set theory, stochastic processes, characterization of distributions and statistics, percolation theory, iterated function systems and spin glasses. He has lectured at several places in India and abroad.

• 1. Measure Theory: Why and What.- 2. Measures: Construction and Properties.- 3. Measurable Functions and Integration.- 4. Random Variables and Random Vectors.- 5. Product Spaces.- 6. Radon-Nikodym Theorem and Lp Spaces.- 7. Convergence and Laws of Large Numbers.- 8. Weak convergence and Central Limit Theorem.- 9. Conditioning: The Right Approach.- 10. Infinite Products.- 11. Brownian Motion: A Brief Journey.