N.Tsilevich, A.Vershik, and M.Yor.
An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process.
C. R. Acad. Sci. Paris, 329, Serie I (1999), 163-168.

Abstract.We define a one-parameter family of sigma-finite (finite on compact sets) measures in the space of distributions. These measures are equivalent to the laws of the classical gamma processes and invariant under an infinite-dimensional abelian group of certain positive multiplicators. This family of measures was first discovered by Gelfand-Graev-Vershik in the context of the representation theory of current groups; here we describe it in direct terms using some remarkable properties of the gamma processes. We show that the class of multiplicative measures coincides with the class of zero-stable measures which is introduced in the paper. We give also a new construction of the canonical representation of the current group SL(2,R)^X.

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