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Category Analogue of Sup-Measurability Problem
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K. Ciesielski
Published/Copyright:
June 7, 2010
Abstract
A function 
is called sup-measurable if Fƒ : ℝ → ℝ given by Fƒ(x) = F(x, ƒ(x)), x ∈ ℝ, is measurable for each measurable function ƒ : ℝ → ℝ. It is known that under different set theoretical assumptions, including CH, there are sup-measurable non-measurable functions, as well as their category analogues. In this paper we will show that the existence of the category analogues of sup-measurable non-measurable functions is independent of ZFC. A similar result for the original measurable case is the subject of a work in prepartion by Ros lanowski and Shelah.
Received: 1999-09-03
Revised: 2000-04-11
Published Online: 2010-06-07
Published in Print: 2000-December
© Heldermann Verlag
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Articles in the same Issue
- Category Analogue of Sup-Measurability Problem
- Lipschitzian Superposition Operators Between Spaces of Functions of Bounded Generalized Variation with Weight
- The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
- Graph Convergence of Set-Valued Maps and its Relationship to Other Convergences
- Local Existence of Solutions of a Free Boundary Problem for Equations of Compressible Viscous Heat-Conducting Capillary Fluids
- Quotients of Quasi-Continuous Functions
- Integrals of Legendre Polynomials and Solution of Some Partial Differential Equations
- Existence Theorems for Maximal Elements in H-Spaces with Applications on the Minimax Inequalities and Equilibrium of Games
- On Continuity of Measurable Cocycles
