Searching for structures inside of the family of bounded derivatives which are not Riemann integrable. (English) Zbl 1450.46014

Summary: We construct a non-separable Banach space every nonzero element of which is a bounded derivative that is not Riemann integrable. This in particular improves a result presented in [D. García et al., Math. Nachr. 283, No. 5, 712–720 (2010; Zbl 1210.46019)], where the corresponding space was found to be separable.


46B87 Lineability in functional analysis
46E15 Banach spaces of continuous, differentiable or analytic functions
26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A36 Antidifferentiation
15A03 Vector spaces, linear dependence, rank, lineability


Zbl 1210.46019
Full Text: DOI Euclid


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