Brownian local minima, random dense countable sets and random equivalence classes

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A random dense countable set is characterized (in distribution) by independence and stationarity. Two examples are `Brownian local minima' and `unordered infinite sample'. They are identically distributed. A framework for such concepts, proposed here, includes a wide class of random equivalence classes.
40 pages. Supersedes math.PR/0508414 and math.PR/0511011

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