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Null set
Measurable set whose measure is zero / From Wikipedia, the free encyclopedia
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For the set with no elements, see Empty set.
For the set of zeros of a function, see Zero set.
In mathematical analysis, a null set is a Lebesgue measurable set of real numbers that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length.
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The notion of null set should not be confused with the empty set as defined in set theory. Although the empty set has Lebesgue measure zero, there are also non-empty sets which are null. For example, any non-empty countable set of real numbers has Lebesgue measure zero and therefore is null.
More generally, on a given measure space a null set is a set
such that