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- In measure theory, given a measurable space and a signed measure on it, a set is called a positive set for if every -measurable subset of has nonnegative measure; that is, for every that satisfies holds. Similarly, a set is called a negative set for if for every subset satisfying holds. Intuitively, a measurable set is positive (resp. negative) for if is nonnegative (resp. nonpositive) everywhere on Of course, if is a nonnegative measure, every element of is a positive set for In the light of Radon–Nikodym theorem, if is a σ-finite positive measure such that a set is a positive set for if and only if the Radon–Nikodym derivative is nonnegative -almost everywhere on Similarly, a negative set is a set where -almost everywhere. (en)
- In matematica, un insieme si dice positivo (rispettivamente negativo) rispetto alla misura con segno se ogni suo sottoinsieme ha misura non negativa (rispettivamente non positiva). (it)
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- 3258 (xsd:nonNegativeInteger)
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- In matematica, un insieme si dice positivo (rispettivamente negativo) rispetto alla misura con segno se ogni suo sottoinsieme ha misura non negativa (rispettivamente non positiva). (it)
- In measure theory, given a measurable space and a signed measure on it, a set is called a positive set for if every -measurable subset of has nonnegative measure; that is, for every that satisfies holds. Similarly, a set is called a negative set for if for every subset satisfying holds. Intuitively, a measurable set is positive (resp. negative) for if is nonnegative (resp. nonpositive) everywhere on Of course, if is a nonnegative measure, every element of is a positive set for (en)
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- Insieme positivo e insieme negativo (it)
- Positive and negative sets (en)
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