Editing Absolute continuity (section)

===Definition===
A [[Measure (mathematics)|measure]] <math>\mu</math> on [[Borel set|Borel subsets]] of the real line is absolutely continuous with respect to the [[Lebesgue measure]] <math>\lambda</math> if for every <math>\lambda</math>-measurable set <math>A,</math> <math>\lambda(A) = 0</math> implies <math>\mu(A) = 0</math>. Equivalently,  <math>\mu(A) > 0</math> implies <math>\lambda(A) > 0</math>. This condition is written as <math>\mu \ll \lambda.</math> We say <math>\mu</math> is ''dominated'' by <math>\lambda.</math>

In most applications, if a measure on the real line is simply said to be absolutely continuous — without specifying with respect to which other measure it is absolutely continuous — then absolute continuity with respect to the Lebesgue measure is meant.

The same principle holds for measures on Borel subsets of <math>\mathbb{R}^n, n \geq 2.</math>