of axioms for affine ${\mathbb{R}}$- buildings have been previously studied by Anne Parreau [@Parreau]. This paper extends her results. Further did the author have access to a preprint by Curt Bennett [@Bennett2] which is also devoted to a reduction of the axioms of a generalized affine buildings. He did replace the difficult to verify (A6) by easier alternatives.

The original axiomatic definition of affine buildings is due to Jaques Tits. He defined the “syst[è]{}me d’appartements” in [@TitsComo] by listing five axioms. The first four of these are precisely axioms $(A1)-(A4)$ as presented in the following section. His fifth axiom originally reads different from ours but was later replaced with what is now axiom (A5) in Definition \[Def\_LambdaBuilding\]. The interested reader can find a short history of Tits’ axioms in Marc Roman’s book [@Ronan]. As already mentioned above in 1994 Bennett introduced the notion of a generalized affine building, by adding an additional axiom to Tits’ list. He gave an example showing that the new axiom (A6) might not be omitted.

Assuming that the metric induced by the Euclidean distance on one apartment satisfies the triangle inequality, Anne Parreau later proved equivalence of (A5) and (A6) in case $\Lambda={\mathbb{R}}$. In her 