Nullset
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.
A null set is not to 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
M
=
(
X
,
Σ
,
μ
)
{\displaystyle M=(X,\Sigma ,\mu )}
a null set is a set
S
∈
Σ
{\displaystyle S\in \Sigma }
such that
μ
(
S
)
=
0.
{\displaystyle \mu (S)=0.}
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