Abstract
With a measure ϕ on a σ-algebra Σ of sets taking values in a Ba- nach space two positive functions on Σ, called semivariations of ϕ, are asso- ciated. We characterize those functions as order continuous submeasures that are multiply subadditive in the sense of G. G. Lorentz (1952). In connection with some results of G. Curbera (1994) and the author (2003), we also discuss the special cases where ϕ is separable and nonatomic or has relatively compact range.
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Dedicated to Professor Heinz König on his 80th birthday
Communicated by L. Kérchy
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Lipecki, Z. Semivariations of a vector measure. ActaSci.Math. 76, 411–425 (2010). https://doi.org/10.1007/BF03592961
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DOI: https://doi.org/10.1007/BF03592961
Key words and phrases
- Banach space
- vector measure
- semivariation
- relatively compact range
- separable
- nonatomic
- submeasure
- order continuous
- multiply subadditive