Abstract
Inequalities are established among certain binary operations on a space of probability distribution functions. These operations arise naturally in the theory of probabilistic metric spaces, in the generalized theory of information, and in other contexts of the theory of probability. It is further shown that, in most cases, equality holds in the inequalities if and only if at least one of the arguments is a unit step function, i.e., that the associated functional equations have in general only essentially trivial solutions.
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© 1978 Springer Basel AG
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Moynihan, R., Schweizer, B., Sklar, A. (1978). Inequalities Among Operations on Probability Distribution Functions. In: Beckenbach, E.F. (eds) General Inequalities 1 / Allgemeine Ungleichungen 1. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5563-1_13
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DOI: https://doi.org/10.1007/978-3-0348-5563-1_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5565-5
Online ISBN: 978-3-0348-5563-1
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