Abstract
A family of identities primarily associated with isoperimetric inequalities for planar convex domains was discovered by Pleijel in 1956. We call these identities classical Pleijel identities. R. V. Ambartzumian gave combinatorial proof of these identities and pointed out that they can be applied to find chord length distribution functions for convex domains. In the classical Pleijel identities integration is over the measure in the space \( \mathbb{G} \) of lines which is invariant with respect to the all Euclidean motions. In the present paper they are considered for any locally-finite measure in the space \( \mathbb{G} \). These identities are applied to find the so-called orientation-dependent chord length distribution (or density) functions for bounded convex domains.
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