m-almost-metrization for APM spaces

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In this paper, we have discussed what kind of the almost -probability-metrizabe spaces ad-mits their topology be generated by a family of pseudo-metrics, that is , the generalized metrizable prob-lem , and proved the following theorems :Theorem 1 Every APM space is m-almost-metrizable.Theorem 2 The product APM space of a family of the completion spaces of APM spoces is thecompletion of the product APM space of the family of APM spaces.