  The overlap formalism of chiral fermions provides a tool to measure the
index, Q, of the chiral Dirac operator in a fixed gauge field background on the
lattice. This enables a numerical measurement of the probability distribution,
p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure
SU(2) gauge theory by measuring Q on 140 independent gauge field configurations
generated on a 12^4 lattice using the standard single plaquette Wilson action
at a coupling of beta=2.4. This distribution is in good agreement with a recent
measurement [8] of the distribution of the topological charge on the same
lattice using the same coupling and the same lattice gauge action. In
particular we find <Q^2>=3.3(4) to be compared with <Q^2> = 3.9(5) found in
[8]. The good agreement between the two distributions is an indication that the
continuum index theorem can be carried over in a probabilistic sense on to the
lattice.
