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.

通过证明普罗霍罗夫度量中的有效收敛等价于有效弱收敛，我们扩展了实线上测度弱收敛的有效框架。此外，我们还建立了措施模糊趋同有效理论的研究框架。我们引入了模糊收敛的一致概念和非一致概念，并证明这两个概念是等价的。然而，有效模糊收敛下的极限即使是有限的也可能无法计算。我们给出了一个有限的不可计算的有效模糊极限测度的例子，并且我们提供了一个充分必要条件，使得有效模糊收敛产生一个可计算的极限。最后，我们确定了措施的有效弱收敛和模糊收敛一致的充分条件。作为推论，