Cameron-Martin theorems for sequences of symmetric Cauchy-distributed random variables

Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale parameter sequences. Using a result of Kakutani on equivalence of infinite product measures, we provide sufficient conditions for the equivalence of laws of the two sequences.
Comment: This paper has been withdrawn by the author because it is superseded by the article "Quasi-invariance of countable products of Cauchy measures under translations and non-unitary dilations" (arXiv:1611.10289)