An earlier introduced characterization of nonuniform learnability that allows the sample size to depend on the hypothesis to which the learner is compared has been redefined using the measure theoretic approach. Where nonuniform learnability is a strict relaxation of the Probably Approximately Correct framework. Introduction of a new algorithm, Generalize Measure Learnability framework, to implement this approach with the study of its sample and computational complexity bounds. Like the Minimum Description Length principle, this approach can be regarded as an explication of Occam razor. Furthermore, many situations were presented, Hypothesis Classes that are countable where we can apply the GML framework, which we can learn to use the GML scheme and can achieve statistical consistency.