TITLE: about measure theory
QUESTION [1 upvotes]: If A and B are disjoint subsets of real numbers, and one of them is measurable can we say
m*(A U B)=m*(A)+m*(B)?
I am unable to find counter example. I feel this is not true.

REPLY [6 votes]: This is true.  If for example  A is measurable it is measurable in the sense of Caratheodory so that
For every set C we will have 
$m*(C) = m*(C\cap A) + m*(C \setminus A)$.
This with $C=A \cup B$  is your assertion
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