AI 中文总结
针对前向Funk球上beta测度的锥形极限问题，构造了qm-空间的锥形紧度量空间，证明相关伴随锥形映射是1-利普希茨拓扑嵌入且像稠密，还得出qm-空间的盒-距离空间完备可分的次要结论。
AI 中文摘要
拟度量测度空间（qm-空间）是一类集合，带有定向距离，其对称化是完备可分度量，同时带有满支撑的Borel概率测度。受确定前向Funk球上beta测度的锥形极限问题驱动，我们构造了一个由qm-空间的锥形构成的紧度量空间。从qm-空间的浓度-距离空间到该紧空间的伴随锥形映射是具有稠密像的1-利普希茨拓扑嵌入。作为次要结果，我们证明了qm-空间的盒-距离空间是完备可分的。
英文摘要
A quasi-metric measure space (qm-space) is a set with a directed distance whose symmetrization is a complete separable metric, together with a Borel probability measure of full support. Motivated by the problem of determining the pyramid limits of beta measures on forward Funk balls, we construct a compact metric space of pyramids of qm-spaces. The associated-pyramid map from the concentration-distance space of qm-spaces into this compact space is a $1$-Lipschitz topological embedding with dense image. As a secondary result, we prove that the box-distance space of qm-spaces is complete and separable.
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