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We give a more elementary proof of a result by Ambrosio, Fusco and Hutchinsonto estimate the Hausdorff dimension of the singular set of minimizers of theMumford-Shah energy (see [2, Theorem 5.6]). On the one hand, we follow thestrategy of the above mentioned paper; but on the other hand our analysisgreatly simplifies the argument since it relies on the compactness resultproved by the first two Authors in [4, Theorem 13] for sequences of localminimizers with vanishing gradient energy, and the regularity theory of minimalCaccioppoli partitions, rather than on the corresponding results for Almgren'sarea minimizing sets.

A note on the hausdorff dimension of the singular set for minimizers of the mumford-shah energy