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# Probability laws with 1-stable marginals

**Gennady Samorodnitsky
**

Murad S. Taqqu

### Abstract:

*We show
that if is a vector in and all linear
combinations
are 1-stable random variables, then *** X**
is itself 1-stable. More generally,
a probability measure on a vector space whose univariate
marginals are 1-stable, is itself 1-stable.
This settles an outstanding problem of Dudley and Kanter.