Given two separable Banach spaces  and , a CSM  on  and a continuous linear map , we say that  is radonifying if the push forward CSM (see below)  on  "is" a measure, i.e.
Given two separable Banach spaces are given, along with a continuous linear map and a CSM on one of them, then a CSM is considered to be radonifying if its pushforward onto the other space is a measure.