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On Busemann–Feller extensions of translation invariant density differentiation bases

  • Irakli Japaridze EMAIL logo
Published/Copyright: March 29, 2023
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Abstract

It is known that a translation invariant density differentiation basis B formed of convex sets and its Busemann–Feller extension B BF have similar properties, in particular, the Busemann–Feller extension differentiates the same class of non-negative functions as the basis B. We prove the optimality of the convexity condition in this result.

MSC 2010: 28A15; 42B25

References

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Received: 2022-08-01
Accepted: 2022-09-14
Published Online: 2023-03-29
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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