Vector integrals: The Fubini and Prokhorov theorems.

The article presents a study regarding the vector integrals of the Fubini and Prokhorov Theorems which reduces the lag between locally convex spaces (LCSs) and Banach spaces. It highlights the values in the vector-dual LCS which involves the measure as an abstract measure space and the domain of the function. It states that the Fubini theorem is invalid since the multiplication by the initial transition measure may not commute. It mentions that a criterion in the Prokhorov theorem had no infinite-dimensional analogue which justifies the analogue as a general class of LCSs.