Support vector machines have attracted much attention in theoretical and in
applied statistics. Main topics of recent interest are consistency, learning
rates and robustness. In this article, it is shown that support vector machines
are qualitatively robust. Since support vector machines can be represented by a
functional on the set of all probability measures, qualitative robustness is
proven by showing that this functional is continuous with respect to the
topology generated by weak convergence of probability measures. Combined with
the existence and uniqueness of support vector machines, our results show that
support vector machines are the solutions of a well-posed mathematical problem
in Hadamard's sense.