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<p>Using Calderón–Zygmund techniques, we establish a link between gauge-controlled mean oscillation bounds and Hölder-type continuity. We introduce a gauge-based notion of Lebesgue set and examine its measurability, together with its approximation properties. For power gauges, we prove rectifiability results showing that, up to negligible sets, the graphs of functions on their Lebesgue sets can be covered by countably many Hölder graphs.</p>

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A fine classification of Lebesgue points

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月11日

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  • Silvano Delladio

摘要

Using Calderón–Zygmund techniques, we establish a link between gauge-controlled mean oscillation bounds and Hölder-type continuity. We introduce a gauge-based notion of Lebesgue set and examine its measurability, together with its approximation properties. For power gauges, we prove rectifiability results showing that, up to negligible sets, the graphs of functions on their Lebesgue sets can be covered by countably many Hölder graphs.