By Olav Kallenberg
This is the 1st finished remedy of the 3 simple symmetries of chance concept - contractability, exchangeability, and rotatability - outlined as invariance in distribution lower than contractions, variations, and rotations. Originating with the pioneering paintings of de Finetti from the 1930's, the speculation has advanced right into a specific physique of deep, attractive, and infrequently dazzling effects, comprising the elemental representations and invariance homes in a single and a number of other dimensions, and showing a few unforeseen hyperlinks among a number of the symmetries in addition to to many different components of contemporary chance. so much chapters require just some uncomplicated, graduate point chance concept, and may be available to any critical researchers and graduate scholars in likelihood and records. components of the booklet can also be of curiosity to natural and utilized mathematicians in different components. The exposition is officially self-contained, with precise references supplied for any deeper proof from genuine research or likelihood utilized in the booklet.
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