naa a22 4500 51078268X CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0122-0 doi (NATIONALLICENCE)springer-10.1007/s11856-012-0122-0 Measurability in $$C({2^\kappa })$$ } and Kunen cardinals [Elektronische Daten] [A. Avilés, G. Plebanek, J. Rodríguez] A cardinal κ is called a Kunen cardinal if the σ-algebra on κ × κ generated by all products A×B, where A,B ⊂ κ, coincides with the power set of κ×κ. For any cardinal κ, let $$C({2^\kappa })$$ be the Banach space of all continuous real-valued functions on the Cantor cube $$C({2^\kappa })$$ . We prove that κ is a Kunen cardinal if and only if the Baire σ-algebra on $$C({2^\kappa })$$ for the pointwise convergence topology coincides with the Borel σ-algebra on $$C({2^\kappa })$$ for the norm topology. Some other links between Kunen cardinals and measurability in Banach spaces are also given. Hebrew University Magnes Press, 2013 Avilés A. Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100, Espinardo (Murcia), Spain aut Plebanek G. Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland aut Rodríguez J. Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100, Espinardo (Murcia), Spain aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 1-30 0021-2172 195:1<1 2013 195 11856 https://doi.org/10.1007/s11856-012-0122-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0122-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Avilés A. Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100, Espinardo (Murcia), Spain aut NATIONALLICENCE 700 1- Plebanek G. Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland aut NATIONALLICENCE 700 1- Rodríguez J. Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100, Espinardo (Murcia), Spain aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/1(2013-06-01), 1-30 0021-2172 195:1<1 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer