What is Luzin N property?

In mathematics, a function f on the interval has the Luzin N property, named after Nikolai Luzin if for all N ⊂ {\displaystyle N\subset } such that λ = 0 {\displaystyle \lambda =0} , there holds: λ ] = 0 {\displaystyle \lambda ]=0} , where λ {\displaystyle \lambda } stands for the Lebesgue measure.

Note that the image of such a set N is not necessarily measurable, but since the Lebesgue measure is complete, it follows that if the Lebesgue outer measure of that set is zero, then it is measurable and its Lebesgue measure is zero as well.