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Abstract: In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator , , where a is a piecewise continuous function on the unit circle. We prove that the behavior of the approximation numbers of the finite sections depends heavily on the Fredholm properties of the operators and . In particular, if the operators and are Fredholm on , then the approximation numbers of have the so-called k-splitting property. But, in contrast with the case of continuous symbols, the splitting number k is in general larger than . [Copyright &y& Elsevier]