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The dependence of the Cherenkov radiation intensity o f e + e pairs produced by high energy -quanta on the distance z from the pair production point, the radiator thickness L, and the azimuthal angle ' of the observation point from the -quanta linear polarization direction, is calculated, taking into account the multiple scattering. It is shown that the measurement of the -quanta polarization by detection of the expected '-asymmetry with the help of a RICH detector is easier than with other existing or proposed methods.