Abstract
The set of Lebesgue points of a locally integrable function on -dimensional Euclidean space , , is an -set of full measure. In this article it is shown that every -set of full measure is the set of Lebesgue points of some measurable bounded function, and, further, that a set with these properties is the set of points of convergence and nontangential (stable) convergence of a singular integral of convolution type:
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