Lebesgue measurable sets are the subsets of {% \mathbb{R}^n %} that can be assigned a consistent measure.
The concept is generalized as
Let {% E \subset \mathbb{R}^n %}
then {% E %} is measurable if
{% m^*(A) = m^*(A\cap E) + m^*(A \backslash E) %}
for all {% A \subset \mathbb{R}^n %}
