  We expand our effective framework for weak convergence of measures on the
real line by showing that effective convergence in the Prokhorov metric is
equivalent to effective weak convergence. In addition, we establish a framework
for the study of the effective theory of vague convergence of measures. We
introduce a uniform notion and a non-uniform notion of vague convergence, and
we show that both these notions are equivalent. However, limits under effective
vague convergence may not be computable even when they are finite. We give an
example of a finite incomputable effective vague limit measure, and we provide
a necessary and sufficient condition so that effective vague convergence
produces a computable limit. Finally, we determine a sufficient condition for
which effective weak and vague convergence of measures coincide. As a
corollary, we obtain an effective version of the equivalence between classical
weak and vague convergence of sequences of probability measures.
