Published online by Cambridge University Press: 26 February 2010
Absolute curvature measures for locally finite unions of sets with positive reach are introduced, extending the definition of Zähle [13] by taking into account the absolute value of the index function. It is shown that this definition differs from that of Matheron [5] and Schneider [12]. An intersection formula of Crofton type for absolute curvature measures is proved. The role of absolute curvature measures in geometric statistics is illustrated by an example.