Multi‐dimensional perspectives on stereology

The structures of primary concern in Part A are varieties—the generalization in higher dimensions of smooth curves and surfaces. Fixed orientation random s‐sections (s‐dimensional flat sections) of a fixed t‐variety (t‐dimensional variety) in Rd (d‐dimensional space) are considered in Section 2. The t‐variety induces a density‐cum‐orientation distribution which is related to corresponding sectional quantities. The by now classical basic formula; of stereology are all special cases of the simple multi‐dimensional formula (2.16). Next (Section 3), statistics of the variety of intersection of several statistically homogeneous random varieties are related to the corresponding statistics of the parent varieties.