Über Wahrscheinlichkeit der Aufdeckung des Gebietes bei Linearer Suche

R. S. Guter

Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 2, pp. 365-367

Résumé

Lying in a circle $G$ is a convex rectifiable region $K$. If a cut $L$ is made in the circle at random then the probability of cutting the region $K$ is $$ P=\frac{\frac2\pi LV(K)+W(K)}{\pi R^2-L\sqrt{R^2-\frac{L^2}4}-R^2\arcsin\frac L{2R}}. $$ Here, $V(K)$ and $W(K)$ are the linear and planar variations of $K$ in the sense of A. S. Kronrod and A. G. Vitushkin.