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The purpose of this paper is to discuss the properties of regularity and strong regularity of fuzzy measure on metric spaces following the previous results. Some properties are defined with the help of nulladditivity such as inner\outer regularity and the regularity of fuzzy measure. We define the strong regularity of fuzzy measures and show our result that the null-additive fuzzy measures possess a strong regularity on complete separable metric spaces.doi:10.6084/m9.figshare.1410999.v1 fatcat:qfpmphzhubhbhhm6mszsyokyjm