Norms supporting the Lebesgue differentiation theorem
classification
🧮 math.FA
keywords
lebesguetheoremdifferentiationnormnormscharacterizedconditionscustomary
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A version of the Lebesgue differentiation theorem is offered, where the $L^p$ norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation theorem are established. In particular, Lorentz, Orlicz and other customary norms for which Lebesgue's theorem holds are characterized.
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