Baire one functions and their sets of discontinuity

• المؤلفون الرئيسيون: Fenecios, Jonald P, Cabral, Emmanuel A, Racca, Abraham P
• التنسيق: text
• منشور في: Archīum Ateneo 2016
• الموضوعات: Mathematics
• الوصول للمادة أونلاين: https://archium.ateneo.edu/mathematics-faculty-pubs/64; https://eudml.org/doc/276786

A characterization of functions in the first Baire class in terms of their sets of discontinuity is given. More precisely, a function f:R→R is of the first Baire class if and only if for each ϵ>0 there is a sequence of closed sets {Cn}∞n=1 such that Df=⋃∞n=1Cn and ωf(Cn)<ϵ for each n where ωf...