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We call $\\mu$ non-defective if $\\mu(\\mathfrak{M}_\\mu) = 0$. The class $M^0(X) \\subset M(X)$ consists of probability measures and infinite non-defective measures. We classify measures $\\mu$ from $M^0(X)$ with respect to a homeomorphism. The notions of goodness and compact open values set $S(\\mu)$ are defined. 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