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arXiv · 1806.05535

On the differentiation of integrals with respect to translation invariant convex density bases

Giorgi Oniani
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Abstract

For a translation invariant convex density basis $B$ it is shown that its Busemann-Feller extension $B_{\mathrm{BF}}$ has close to $B$ properties, in particular, $B_{\mathrm{BF}}$ differentiates the same class of non-negative functions as $B$. Using the similarity between properties of the bases $B$ and $B_{\mathrm{BF}}$ some results known for Busemann-Feller bases are transferred to bases without restriction of being Busemann-Feller.

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Giorgi Oniani. 2018-06-14. On the differentiation of integrals with respect to translation invariant convex density bases. https://arxiv.org/abs/1806.05535

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