The inverse theorem of Luzin's theorem is a theorem of real analysis, which roughly means that the measurable function is almost continuous.

Luzin problem, a mathematical research term, also known as Luzin conjecture, is a famous problem in Fourier series theory. He pointed out that it is not clear whether even the Fourier series of a continuous function must have a convergence point. He considered the problem from the perspective of denying Luzin's conjecture.