 Given two separable Banach spaces formula_1 and formula_2, a CSM formula_3 on formula_1 and a continuous linear map formula_5, we say that formula_6 is "radonifying" if the push forward CSM (see below) formula_7 on formula_2 "is" a measure, i.e.there is a measure formula_9 on formula_2 such that
for each formula_12, where formula_13 is the usual push forward of the measure formula_9 by the linear map formula_15.Because the definition of a CSM on formula_2 requires that the maps in formula_17 be surjective, the definition of the push forward for a CSM requires careful attention.