## B. Tsirelson | ## Brownian local minima, random dense countable sets and random equivalence classes | ## Recent works |

Boris Tsirelson,

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

Electronic Journal of Probability **11**:7, 162-198 (2006).

Available online (free of charge) on the journal site:

http://www.math.washington.edu/~ejpecp/EjpVol11/paper7.abs.html

See also
arXiv.org/abs/math.PR/0601673/

A research paper, 37 pages, bibl. 15 refs.

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.

- Introduction.
- Main lemma.
- Random countable sets.
- Selectors.
- Independence.
- Selectors and independence.
- Main results.
- Borelogy, the new framework.
- Probability measures on singular spaces.
- Some generalizations and final remarks.

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