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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 ...
This book is based on a course of lectures given to PhD students at the Delhi Centre of the Indian Statistical Institute during the years 1980-1985. The approach is inspired by the lectures of G.W. Mackey and V.S. Varadarajan and brings out the role of group representations as the main thread passing through some major results like Gleason's theorem on the characterization of quantum states, Wigner's Unitarity-antiunitarity theorem on the automorphisms for the ...
The aim of this little book is to convey three principal developments in the evolution of modern information theory: Shannon's initiation of a revolution in 1948 by his interpretation of the Boltzmann entropy as a measure of information yielded by an elementary statistical experiment and his basic coding theorems on storage and optimal transmission of messages through noisy communication channels; the influence of ergodic theory in the enlargement of the scope of ...