  Milnor-Thurston homology theory is a construction of homology theory that is
based on measures. It is known that it is equivalent to singular homology
theory in case of manifolds and complexes. Its behaviour for non-tame spaces is
still unknown. This paper provides results in this direction. We prove that
Milnor-Thurston homology groups for the Warsaw Circle are trivial except for
the zeroth homology group which is uncountable dimensional. Additionally, we
prove that the zeroth homology group is non-Hausdorff for this space with
respect a natural topology that was proposed by Berlanga.
