On the complexity of sums of Dirichlet measures

Kahane, Sylvain. "On the complexity of sums of Dirichlet measures." Annales de l'institut Fourier 43.1 (1993): 111-123. <http://eudml.org/doc/74983>.

@article{Kahane1993,
abstract = {Let $M$ be the set of all Dirichlet measures on the unit circle. We prove that $M+M$ is a non Borel analytic set for the weak* topology and that $M+M$ is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates $M+M$ from $D^ \bot $ (or even $L^\bot _0)$, the set of all measures singular with respect to every measure in $M$. This extends results of Kaufman, Kechris and Lyons about $D^\bot $ and $H^\bot $ and gives many examples of non Borel analytic sets.},
author = {Kahane, Sylvain},
journal = {Annales de l'institut Fourier},
keywords = {singular measures; Dirichlet measures on the unit circle; non Borel analytic set; weak* Borel set},
language = {eng},
number = {1},
pages = {111-123},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the complexity of sums of Dirichlet measures},
url = {http://eudml.org/doc/74983},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Kahane, Sylvain
TI - On the complexity of sums of Dirichlet measures
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 1
SP - 111
EP - 123
AB - Let $M$ be the set of all Dirichlet measures on the unit circle. We prove that $M+M$ is a non Borel analytic set for the weak* topology and that $M+M$ is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates $M+M$ from $D^ \bot $ (or even $L^\bot _0)$, the set of all measures singular with respect to every measure in $M$. This extends results of Kaufman, Kechris and Lyons about $D^\bot $ and $H^\bot $ and gives many examples of non Borel analytic sets.
LA - eng
KW - singular measures; Dirichlet measures on the unit circle; non Borel analytic set; weak* Borel set
UR - http://eudml.org/doc/74983
ER -