I have reached the titled chapter of "Probability Measures on Metric Spaces" and quickly became disoriented. Obviously, reading Parthasarathy's book requires considerable preparation, some of which I have. However, the formula for the "distribution of a totally finite measure" and the subsequent (to me, out of nowhere) formula for the characteristic function of said measure's "distribution" is baffling. Consulting my references does not help, and I do not have a clue where to look. Any recommendation for background material would be most appreciated. The author is very terse, especially with regard to notation and references. I have dozens of Probability, Topology, Analysis references already (including Gnedenko and Kolomorgorov, Lukacs, Rudin, Kelly, Loeve, Doob, and more). I have never seem anything similar to the material in Parthasarathy's book before. My goal was/is to understand Sazonov's theorem, but I would love to read this work in full. Thank you. Gary
2026-04-03 14:48:49.1775227729
Measures on Locally Compact Abelian Groups - Chapter in Parthasarathy
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After obtaining access to the author's previously published work, and other related works in journals, I have been able to decode the notation and gain additional contectual background. It does appear that the book is one of a kind for the content it covers. Any suggested additional resources would of course still be appreciated.