In this note, we prove that the countable compactness of {0, 1} R together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.
Wenn "Jan Lucemburský" auf "Jhang de Blannen" trifft: ein Vergleich der Darstellungsformen König Johanns von Böhmen in den tschechischen Landen und Luxemburg.
We tested the hypothesis that males of meadow pipits (Anthus pratensis) respond differentially to simulated territorial intrusions (song playback + bird model) by conspecific, related (tree pipit, Anthus trivialis), and unrelated individuals (willow warbler, Phylloscopus trochilus), and evaluated the effect of playback order. All tested males responded aggressively to the conspecific playback; reactions to heterospecific stimuli occurred only after previous excitation by the conspecific song and dummy, and were usually weaker. Apparently, although males were able to discriminate between playbacks, excitation by intrusion of a conspecific rival elicited an aggressive reaction to otherwise neutral stimuli. Reactions to heterospecific playbacks closely following the conspecific one did not differ significantly between congeneric and unrelated species. The response to a subsequent heterospecific stimulus, however, was taxon-dependent: congeneric species elicited a significantly stronger reaction than an unrelated one. We presume that this was due to the morphological similarity between pipits, and that the more intensive reaction could have been caused by stronger visual stimulus from the respective model. We discuss the potential benefits as well as limitations of using models (dummies) in playback experiments, and suggest that overexcitation by previous stimuli should be considered during experimental setup and data analysis in studies focusing both on interspecific aggressiveness and on neighbour-stranger interactions.