# Luzin N property

In mathematics, a function f on the interval [a, b] has the Luzin N property, named after Nikolai Luzin (also called Luzin property or N property) if for all ${\displaystyle N\subset [a,b]}$ such that ${\displaystyle \lambda (N)=0}$, there holds: ${\displaystyle \lambda (f(N))=0}$, where ${\displaystyle \lambda }$ stands for the Lebesgue measure.