Nonatomic problems of location of extended objects

The paper is concerned with optimal siting, in a specified region $D$, of a certain continuum $\Omega$. The length $\omega\in\Omega$ of the objects is modeled by specifying a measure on the $\sigma$-algebra of subsets from $\Omega$. It is required to find an invective mapping $\varphi:\Omega\to D$ which maintains the measure and minimizes the functional dependent on $\omega$ and denoting the mean const of communications linking elements from $\Omega$. Examples are considered.