A1-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions
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DOI: 10.1007/s10958-018-3698-z
Abstract: Let X be a Banach lattice of measurable functions on ℝn × Ω having the Fatou property. We show that the boundedness of all Riesz transforms Rj in X is equivalent to the boundedness of… read more here.
Keywords: measurable functions; boundedness riesz; riesz transforms; boundedness ... See more keywords
Distance of convergence in measure on spaces of measurable functions
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DOI: 10.1007/s11117-018-0621-2
Abstract: In this paper we investigate the distance of convergence in measure whenever the measure is not $$\sigma $$σ-finite and identify the topological coreflection of this approach structure with a direct proof. Also we investigate its… read more here.
Keywords: measurable functions; distance convergence; convergence measure; measure ... See more keywords
The algebras of bounded and essentially bounded Lebesgue measurable functions
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DOI: 10.1515/dema-2017-0010
Abstract: Abstract Let X be a set in ℝn with positive Lebesgue measure. It is well known that the spectrum of the algebra L∞(X) of (equivalence classes) of essentially bounded, complex-valued, measurable functions on X is… read more here.
Keywords: measurable functions; extremely disconnected; essentially bounded; topology ... See more keywords
On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
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DOI: 10.1515/ms-2017-0073
Abstract: Abstract Let Ω be a Lebesgue-measurable set in ℝn of finite positive Lebesgue measure. In this note we calculate the lack of equi-measurability of the set Kc(Ω), c > 0, of all Lebesgue-measurable functions f… read more here.
Keywords: measurable functions; measurability certain; lack equi; equi measurability ... See more keywords
Spaces of Bounded Measurable Functions Invariant under a Group Action
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DOI: 10.3390/axioms11100505
Abstract: In this paper, we characterize spaces of L∞-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work is analogous to established results concerning invariant spaces of continuous… read more here.
Keywords: topology; measurable functions; group action; spaces bounded ... See more keywords