Following the idea of the Bouyssou-Marchant independence axiom, a basic independence axiom for an indicator is introduced. It is shown that the average number of citations nor the h-index satisfy this basic axiom. Among the indicators considered here only the number of publications and the number of citations satisfy the requirements of this axiom. Weaker forms of the basic independence axiom are considered. The number of citations of the most-cited article satisfies these weaker forms. When studying the h-index the notion of an h-critical publication is introduced.

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