Overview
Absolute Continuity
Given two measures {% \nu %} and {% \mu %} on {% (X,A) %}, {% \nu %} is absolutely continuous with respect to {% \mu %}, written as
{% \nu < < \mu %}
if all the sets with measure zero with respect to {% \mu %} have measure zero with respect to {% \nu %}.
Equivalent Measures
Two measures {% \nu %} and {% \mu %} on {% (X,A) %} are defined to be equivalent if
{% \nu < < \mu %}
and
{% \mu < < \nu %}
That is, two measures are equivalent if they agree on which sets have measure zero.