Vector spaces of non-measurable functions

DOI10.1007/s10114-005-0726-yzbMath1126.28002OpenAlexW2072463698MaRDI QIDQ882750

Francisco Javier García-Pacheco, Juan B. Seoane-Sepúlveda

Publication date: 24 May 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0726-y

zbMATH Keywords

Banach spacedensity characterspaceabilitylineabilitynon-measurable function

Mathematics Subject Classification ID

Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Banach spaces of continuous, differentiable or analytic functions (46E15) Linear function spaces and their duals (46E99)

Related Items

Lineability in subsets of measure and function spaces ⋮ Lineability of the set of supporting vectors ⋮ Strong algebrability of sets of sequences and functions ⋮ Algebraic genericity within the class of sup-measurable functions ⋮ Moduleability, algebraic structures, and nonlinear properties ⋮ Universal Taylor series with maximal cluster sets ⋮ Riemann integrability and Lebesgue measurability of the composite function ⋮ Lineability and spaceability for the weak form of Peano’s theorem and vector-valued sequence spaces ⋮ Linear subsets of nonlinear sets in topological vector spaces

Cites Work

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• Classical Banach spaces. 1: Sequence spaces. 2. Function spaces.
• Algebrability of the set of everywhere surjective functions on \(\mathbb C\)
• Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
• Lineability and spaceability of sets of functions on $\mathbb {R}$
• Every Separable Banach Space is Isometric to a Space of Continuous Nowhere Differentiable Functions