Measurable set wikipedia
How can the answer be improved?measurable set[mezhrbl set (mathematics) A member of the sigmaalgebra of subsets of a measurable space. Measurable Set (in the original meaning), a set to which the definition of measure given by the French mathematician H. Lebesgue is applicable. Measurable sets are one of the principal concepts of the theory of functions of a real measurable set wikipedia
However in definition 1 we call any set like that just measurable, and that given any sigma algebra \Sigma \, \exists \mu an outer measure s. t. the sigma algebra formed by definition 2 with this outer measure is \Sigma.
Universally measurable set's wiki: In mathematics, a subset A displaystyle A of a Polish space X displaystyle X is universally measurable if it is measurable with respect to every complete probability measure on X displayst Nonmeasurable set's wiki: In mathematics, a nonmeasurable set is a set which cannot be assigned a meaningful size . The mathematical existence of such sets is construed to provide information about the notions of length, area and volume in formal set theory.measurable set wikipedia A measurable set X is called a null set if (X)0. A subset of a null set is called a negligible set. A negligible set need not be measurable, but every measurable negligible set is automatically a null set. A measure is called complete if every negligible set is measurable.