度量空间大小的启发式计算和计算机计算
Heuristic and computer calculations for the magnitude of metric spaces
摘要：
紧度量空间的大小的概念是在arXiv：0908.1582中与Tom Leinster一起考虑的，其中大小是针对线段、圆和康托集计算的。本文提供了更多的证据证明一个几何测度理论赋值的关系。首先，给出了一个启发式推导出这个估值考虑“大”子空间的欧几里得空间，其次，数值逼近的大小计算的广场，磁盘，立方体，圆环，环面和Sierpinski垫片。的估值被认为是非常接近的大小为凸空间考虑，并被认为是“渐近”接近其他一些空间。
英文摘要：
The notion of the magnitude of a compact metric space was considered in arXiv:0908.1582 with Tom Leinster, where the magnitude was calculated for line segments, circles and Cantor sets. In this paper more evidence is presented for a conjectured relationship with a geometric measure theoretic valuation. Firstly, a heuristic is given for deriving this valuation by considering 'large' subspaces of Euclidean space and, secondly, numerical approximations to the magnitude are calculated for squares, disks, cubes, annuli, tori and Sierpinski gaskets. The valuation is seen to be very close to the magnitude for the convex spaces considered and is seen to be 'asymptotically' close for some other spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
