MEAN-VALUES OF WEIGHTED CELLS OF STATIONARY POISSON HYPERPLANE TESSELLATIONS OF IRD

This paper deals with stationary Poisson hyperplane tessellations. Wei ghted distributions are considered, where the weights are the volume o f the cell and the total volume of all faces of the cell. A randomly c hosen cell according to such a weighted distribution will be called vo lume weighted cell and face content weighted cell, respectively. Mean values of cell characteristics for such weighted cells are calculated. These results are connected with second-order quantities for the typi cal cell of a stationary Poisson hyperplane tessellation. There are no suppositions to the isotropy of the tessellation, stationarity is suf ficient. In case of isotropy already known results for planar tessella tions from [AMS], [Mi1] and [Mi2] will be confirmed. A stereological i nterpretation of weighted cells is given by the aid of suitable inters ections.