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In this paper we provided a classification for partitions of intervals on thehyperbolic plane. Given a partition, to be named strong, we define a notion ofa hyperbolic-valued functions of bounded variation and a kind ofRiemann-Stieltjes integral. A condition relating to both concepts appears to benatural for the existence of the integral, as it occurs in real analysis.

On the Notion of a Function of Bounded Variation and of Riemann-Stieltjes Integral with Strong Partitions on Hyperbolic Intervals