Geodesic
On the definition of $B$-points
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 219-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is devoted to the study of the so-called Bourgain points ($B$-points) of functions in $L^\infty(\mathbb R)$. In 1993, Bourgain showed that for real-valued bounded function $f$ the set $E_f$ of $B$-points is everywhere dense and has maximal Hausdorff dimension, $\dim_H(E_f)=1$; also the vertical variation of the harmonic extension of $f$ to the upper half-plane is finite at $B$-points. An essentially simpler definition of $B$-points is given compared with the original works by Bourgain. A geometric characterization of the $B$-points of Cantor-like sets is obtained. Bibl. – 7 titles. 
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P. A. Mozolyako. On the definition of $B$-points. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 36, Tome 355 (2008), pp. 219-236. http://geodesic.mathdoc.fr/item/ZNSL_2008_355_a9/

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