Null set

Common card · No. 404647

In mathematical analysis, a null set in R {\displaystyle \mathbb {R} } 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 )...

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