A measure is absolutely continuous with respect to another measure if for every set with . This makes sense as long as is a positive measure, such as Lebesgue measure, but can be any measure, possibly a complex measure.

By the Radon-Nikodym theorem, this is equivalent to saying that

where the integral is the Lebesgue integral, for some integrable function . The function is like a derivative, and is called the Radon-Nikodym derivative .

The measure supported at 0 ( iff ) is not absolutely continuous with respect to Lebesgue measure, and is a singular measure.