Displaying similar documents to “Completely nonmeasurable unions”

On nonmeasurable images

Robert Rałowski, Szymon Żeberski (2010)

Czechoslovak Mathematical Journal

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Let ( X , 𝕀 ) be a Polish ideal space and let T be any set. We show that under some conditions on a relation R ⊆ T 2 × X it is possible to find a set A ⊆ T such that R ( A 2 ) is completely 𝕀 -nonmeasurable, i.e, it is 𝕀 -nonmeasurable in every positive Borel set. We also obtain such a set A ⊆ T simultaneously for continuum many relations ( R α ) α < 2 ω . Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.