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. 
Han Cheng Lie and T. J. Sullivan
math.PR math.ST stat.TH