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References (7)
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- Publisher
- Springer Journals
- Copyright
- Copyright © 1998 by Plenum Publishing Corporation
- Subject
- Mathematics; Mathematics, general
- ISSN
- 1072-947X
- eISSN
- 1572-9176
- DOI
- 10.1007/BF02767994
- Publisher site
- See Article on Publisher Site
Abstract
It is proved that for any given sequence (σ n ,n ∈ ℕ)=Γ0 ⊂ Γ, where Γ is the set of all directions in ℝ2 (i.e., pairs of orthogonal straight lines) there exists a locally integrable functionf on ℝ2 such that: (1) for almost all directionsσ ∈ Γ\Γ0 the integral ∫f is differentiable with respect to the familyB 2σ of open rectangles with sides parallel to the straight lines fromσ: (2) for every directionσ n ∈ Γ0 the upper derivative of ∫f with respect toB 2σ n equals +∞; (3) for every directionσ ∈ Γ the upper derivative of ∫ |f| with respect toB 2σ equals +∞.
Journal
Georgian Mathematical Journal – Springer Journals
Published: Nov 26, 2007