Journal of Mathematical Analysis and Applications· 2026Q1
On Lp-spaces of functions with values in locally convex spaces
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- Q1SCImago
- 2026year
Short summary
This paper introduces pathological phenomena in the nonmetrizable setting of Lusin-measurable functions with values in locally convex spaces, while also establishing density results for associated L p -spaces.
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Key points
- Studies Lusin-measurable functions with values in locally convex spaces.
- Identifies pathological phenomena specific to the nonmetrizable setting.
- Establishes density results for L p -spaces, including simple functions in Hausdorff locally convex spaces.
- Demonstrates convergence through dyadic approximations.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting. Moreover, we establish approximation and density results for L p -spaces constructed with this notion of measurability, including the density of simple functions in Hausdorff locally convex spaces and convergence results obtained through dyadic approximations.
The authors' abstract, as published at the source. Journal of Mathematical Analysis and Applications, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics