Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

A large set containing few orbits of measure preserving transformations

  • 15 Accesses


There exists a Borel set C of product Lebesgue measure one in the Hilbert cube having the property that, for every measure preserving transformationT of the unit interval, allT-orbits contained inC originate from a zero set. This settles an infinite dimensional version of a problem raised by Th. M. Rassias.

This is a preview of subscription content, log in to check access.


  1. [1]

    Iwanik, A.,A property of doubly stochastic densities, Acta Univ. Carolin.—Math. Phys.30 (1989), 65–67.

  2. [2]

    Rassias, Th. M.,Problem 16, 1°, in:Report of the 27th International Symposium on Functional Equations (Problems and Remarks), Aequationes Math.39 (1990), 308.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Iwanik, A. A large set containing few orbits of measure preserving transformations. Aeq. Math. 43, 156–158 (1992).

Download citation

AMS (1980) subject classification

  • 28D05