Structuring Tchebycheff-Type Inequalities – A Systematical Approach / Systematisierung tschebyscheffartiger Ungleichungen – Ein Überblick

Summary Though there is a huge variety of different Tchebycheff-type inequalities in the literature a systematised structuring is missing. The few existing surveys remain rather enumerative. Therefore in this paper a structuring of Tchebycheff-type inequalities is suggested which is based on three complementary criteria, with the type of the available information serving as the main criterion. This structuring is used as a basis for a review on important Tchebycheff-type inequalities, some of which are almost forgotten in the literature. A special emphasis is met on the various relationships between different Tchebycheff-type inequalities, with some figures illustrating the results.