Radonifying function
In measure theory, a radonifying function (ultimately named after Johann Radon) between measurable spaces is one that takes a cylinder set measure (CSM) on the first space to a true measure on the second space. It acquired its name because the pushforward measure on the second space was historically thought of as a Radon measure. Definition. 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. Push forward of a CSM. 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. The CSM is defined by if the composition formula_20 is surjective. If formula_21 is not surjective, let formula_22 be the image of formula_21, let formula_24 be the inclusion map, and define where formula_26 (so formula_27) is such that formula_28. Radonifying function In