<abstract xmlns="http://www.w3.org/1999/xhtml"> We improve and generalize the result of Kirchheim and Natkaniec [Kirchheim, B., Natkaniec, T.: <italic>Exceptional directions for Sierpi´nski’s nonmeasurable</italic><italic>sets</italic>, Fund. Math. <bold>140 </bold>(1992), 237-245] by proving that there exists <italic>D </italic>⊂<italic></italic>[0<italic>, π</italic>) of full outer measure such that the class ∩θ∈D<italic>G</italic>2(<italic>θ</italic>) ∩<italic></italic>∩θ∈[0<italic>,π</italic>)<italic>G</italic>3(<italic>θ</italic>) contains a nonmeasurable set. The present result is obtained within ZFC.</abstract>

We improve and generalize the result of Kirchheim and Natkaniec [Kirchheim, B., Natkaniec, T.: Exceptional directions for Sierpi´nski’s nonmeasurablesets, Fund. Math. 140 (1992), 237-245] by proving that there exists D ⊂[0, π) of full outer measure such that the class ∩θ∈DG2(θ) ∩∩θ∈[0,π)G3(θ) contains a nonmeasurable set. The present result is obtained within ZFC.

Nonmeasurable sets with regular sections

Department of Mathematics Gda´nsk University Wita Stwosza 57 PL–80-952 Gda´nsk POLAND

Tatra Mountains Mathematical Publications

{"article-title":"Nonmeasurable sets with regular sections"}

We improve and generalize the result of Kirchheim and Natkaniec [Kirchheim, B., Natkaniec, T.: Exceptional directions for Sierpi´nski’s nonmeasurablesets,...

Nonmeasurable sets with regular sections

Published Online: Nov 13, 2012

Page range: 79 - 83

DOI: https://doi.org/10.2478/v10127-010-0022-9

Keywords
Sierpi´nski set, nonmeasurable sets on the plane, sections of the plane set

This content is open access.

Nonmeasurable sets with regular sections

Published Online: Nov 13, 2012

Page range: 79 - 83

DOI: https://doi.org/10.2478/v10127-010-0022-9

KeywordsSierpi´nski set, nonmeasurable sets on the plane, sections of the plane set

This content is open access.

Keywords
Sierpi´nski set, nonmeasurable sets on the plane, sections of the plane set