## measure of unbounded set

Suppose A is not a bounded set and m(A∩B)≤(3/4)m(B) for every B. what is m(A)??

here, m is Lebesgue Outer Measure

My attemption is :

Let An=A∩[-n,n], then m(A)=lim m(An)= lim m(An∩[-n,n]) ≤ lim (3/4)m([-n,n]) = infinite.

is my solution right? I am confusing m(A) < infinite , it doest make sence for me. Could someone help me???