Abstract
In this paper, we provide some results related to the Δ2-condition of Musielak–Orlicz functions and ϕ-families of probability distributions, which are modeled on Musielak–Orlicz spaces. We show that if two ϕ-families are modeled on Musielak–Orlicz spaces generated by Musielak–Orlicz functions satisfying the Δ2-condition, then these ϕ-families are equal as sets. We also investigate the behavior of the normalizing function near the boundary of the set on which a ϕ-family is defined.
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Vigelis, R.F., Cavalcante, C.C. (2013). The Δ2-Condition and ϕ-Families of Probability Distributions. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_81
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DOI: https://doi.org/10.1007/978-3-642-40020-9_81
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40019-3
Online ISBN: 978-3-642-40020-9
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