 Intuitively, considering integrals of 'nice' functions, this notion provides more uniformity than weak convergence.As a matter of fact, when considering sequences of measures with uniformly bounded
variation on a Polish space, strong convergence implies the convergence formula_2 for any bounded measurable function formula_3.As before, this convergence is non-uniform in formula_3

The notion of "total variation convergence" formalizes the assertion that the measure of all measurable sets should converge "uniformly", i.e.