Let ##IMG## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn1.gif] {$(\Omega,d)$} be a complete metric space and let ##IMG## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn2.gif] {$\mu$} be a Borel measure on ##IMG## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn3.gif] {$\Omega$} . Under certain fairly general assumptions about the metric and the measure, we use lattice theory to construct an isometric copy ##IMG## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn4.gif] {$(\widetilde\Omega,\widetilde d)$} of the space ##IMG## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn1.gif] {$(\Omega,d)$} , which is called its wave model. The construction is motivated by applications to inverse problems of mathematical physics. We show how the wave model solves the problem of reconstructing a Riemannian mani...

中文翻译：

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带有度量的度量空间的波动模型及其应用

让## IMG ## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn1.gif] {$（\ Omega，d）$}是一个完整的度量空间，并让## IMG ## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn2.gif] {$ \ mu $}是针对## IMG ##的一种Borel度量[http ：//ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn3.gif] {$ \ Omega $}。在有关度量和度量的某些相当普遍的假设下，我们使用格论构建等距副本## IMG ## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn4 .gif] {＃（\ widetilde \ Omega，\ widetilde d）$}的空间## IMG ## [http://ej.iop.org/images/1064-5616/211/4/521/MSB_211_4_521ieqn1。 gif] {$（\ Omega，d）$}，称为其波动模型。该构造是受应用到数学物理反问题的推动。