Given two separableBanach spaces and , a CSM on and a continuouslinear map, we say that is radonifying if the push forward CSM (see below) on "is" a measure, i.e. there is a measure on such that
for each , where is the usual push forward of the measure by the linear map .
Push forward of a CSM
Because the definition of a CSM on requires that the maps in be surjective, the definition of the push forward for a CSM requires careful attention. The CSM
is defined by
if the composition is surjective. If is not surjective, let be the image of , let be the inclusion map, and define
,
where (so ) is such that .
See also
Abstract Wiener space – Mathematical construction relating to infinite-dimensional spaces.