 As applications, we characterize under which conditions the product of a set of probabilities and a set of kernels is compact , and under which conditions a nonlinear version of Fubini's theorem holds true .
<coherence>  As applications, we characterize under which conditions the product of a set of probabilities and a set of kernels is compact , and under which conditions a nonlinear version of Fubini's theorem holds true .
 As applications, we characterize under which conditions the product of a set of probabilities and a set of kernels is compact .