Divergence conditions for Riesz means of Rademacher functions

Some of the divergence conditions for Riesz means of Rademacher functions have been determined. A condition was provided as a criterion for at least one diverging sequence to be summable by the Riesz method. The Rademacher functions can be regarded as independent random variables on the specific probability space with the usual Lebesgue measure. To prove the divergence of a specific number sequence on a set of positive measures, an assertion on the means of Rademacher functions obtained by an arbitrary summation method was considered.