A continuous Helson surface in ${𝐑}^3$

Müller, Detlef. "A continuous Helson surface in ${\bf R}^3$." Annales de l'institut Fourier 34.4 (1984): 135-150. <http://eudml.org/doc/74651>.

@article{Müller1984,
abstract = {For some time it has been known that there exist continuous Helson curves in $\{\bf R\}^2$. This result, which is related to Lusin’s rearrangement problem, had been proved first by Kahane in 1968 with the aid of Baire category arguments. Later McGehee and Woodward extended this result, giving a concrete construction of a Helson $k$-manifold in $\{\bf R\}^\{nk\}$ for $n\ge k+1$. We present a construction of a Helson 2-manifold in $\{\bf R\}^3$. With modification, our method should even suffice to prove that there are Helson hypersurfaces in any $\{\bf R\}^n$.},
author = {Müller, Detlef},
journal = {Annales de l'institut Fourier},
keywords = {Helson set},
language = {eng},
number = {4},
pages = {135-150},
publisher = {Association des Annales de l'Institut Fourier},
title = {A continuous Helson surface in $\{\bf R\}^3$},
url = {http://eudml.org/doc/74651},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Müller, Detlef
TI - A continuous Helson surface in ${\bf R}^3$
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 4
SP - 135
EP - 150
AB - For some time it has been known that there exist continuous Helson curves in ${\bf R}^2$. This result, which is related to Lusin’s rearrangement problem, had been proved first by Kahane in 1968 with the aid of Baire category arguments. Later McGehee and Woodward extended this result, giving a concrete construction of a Helson $k$-manifold in ${\bf R}^{nk}$ for $n\ge k+1$. We present a construction of a Helson 2-manifold in ${\bf R}^3$. With modification, our method should even suffice to prove that there are Helson hypersurfaces in any ${\bf R}^n$.
LA - eng
KW - Helson set
UR - http://eudml.org/doc/74651
ER -