Non-trivial translation-invariant valuations on L^∞

2015/05/01 by Lorenzo Cavallina, Cavallina, Lorenzo
Mathematics · #46E30 (52B45) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1505.00089

openalex publication_date 2015/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Translation-invariant valuations on the space L^∞(ℝⁿ) are examined. We prove that such functionals vanish on functions with compact support. Moreover a rich family of non-trivial translation-invariant valuations on L^∞(ℝⁿ) is constructed through the use of ultrafilters on ℝ.

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