For every p0, there are rectangle-based Busemann-Feller bases on T^ω whose L^p differentiation range is exactly [p0,∞] or (p0,∞], and these ranges exhaust the six possible forms for complete metric measure spaces.
Fern \'a ndez, An \'a lisis de Fourier en el toro infinito-dimensional , Ph.D
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On differentiation of integrals in Lebesgue spaces
For every p0, there are rectangle-based Busemann-Feller bases on T^ω whose L^p differentiation range is exactly [p0,∞] or (p0,∞], and these ranges exhaust the six possible forms for complete metric measure spaces.