Measurable envelopes, Hausdorff measures and Sierpiński sets

Márton Elekes. "Measurable envelopes, Hausdorff measures and Sierpiński sets." Colloquium Mathematicae 98.2 (2003): 155-162. <http://eudml.org/doc/285209>.

@article{MártonElekes2003,
abstract = {We show that the existence of measurable envelopes of all subsets of ℝⁿ with respect to the d-dimensional Hausdorff measure (0 < d < n) is independent of ZFC. We also investigate the consistency of the existence of $ℋ ^\{d\}$-measurable Sierpiński sets.},
author = {Márton Elekes},
journal = {Colloquium Mathematicae},
keywords = {measurable envelope; Hausdorff measure; Sierpiński set; independence},
language = {eng},
number = {2},
pages = {155-162},
title = {Measurable envelopes, Hausdorff measures and Sierpiński sets},
url = {http://eudml.org/doc/285209},
volume = {98},
year = {2003},
}

TY - JOUR
AU - Márton Elekes
TI - Measurable envelopes, Hausdorff measures and Sierpiński sets
JO - Colloquium Mathematicae
PY - 2003
VL - 98
IS - 2
SP - 155
EP - 162
AB - We show that the existence of measurable envelopes of all subsets of ℝⁿ with respect to the d-dimensional Hausdorff measure (0 < d < n) is independent of ZFC. We also investigate the consistency of the existence of $ℋ ^{d}$-measurable Sierpiński sets.
LA - eng
KW - measurable envelope; Hausdorff measure; Sierpiński set; independence
UR - http://eudml.org/doc/285209
ER -