Given a countable set of families \(\{\mathcal{D}_{k}:k \in \mathbb{N}\}\) of pseudometrics over the same set \(D\), we study the power-aggregations of this class, that are defined as convex combinations of integral averages of powers of the elements of \(\cup _{k} \mathcal{D}_{k}\). We prove that a Lipschitz function \(f\) is dominated by such a power-aggregation if and only if a certain property of super-additivity involving the powers of the elements of \(\cup _{k} \mathcal{D}_{k}\) is fulfilled by \(f\). In particular, we show that a pseudo-metric is equivalent to a power-aggregation of other pseudometrics if this kind of domination holds. When the super-additivity property involves a \(p\)-power domination, we say that the elements of \(\mathcal{D}_{k}\) are \(p\)-concave. As an application of our results, we prove under this requirement a new extension result of McShane-Whitney type for Lipschitz \(p\)-concave real valued maps.

给定相同集合\（D \）上一组可计数的伪度量族\（\ {\ mathcal {D} _ {k}：k \ in \ mathbb {N} \} \），我们研究幂集合定义为\（\ cup _ {k} \ mathcal {D} _ {k} \）元素的幂的整数平均值的凸组合。我们证明，当且仅当涉及\（\ cup _ {k} \ mathcal {D}元素的幂的超可加性的某些属性时，Lipschitz函数\（f \）才由这种幂集合控制。_ {k} \）由\（f \）满足。特别是，我们证明了，如果这种支配地位成立，则伪度量等效于其他伪度量的功率聚集。当超可加性涉及\（p \）-幂控制时，我们说\（\ mathcal {D} _ {k} \）的元素是\（p \）-凹面。作为我们结果的应用，我们证明了在此要求下针对Lipschitz \（p \）-凹实值映射的McShane-Whitney类型的新扩展结果。