Interactions between Hlawka Type-1 and Type-2 quantities

The classical Hlawka inequality possesses deep connections with zonotopes and zonoids in convex geometry, has been related to Minkowski space. We introduce Type-1 Type-2 quantities, establish a Hlawka-type relation between them, which connects vast number of strikingly different variants the inequalities, such as Serre's reverse future cone space, for subadditive function on abelian group by Ressel, integral analogs Takahasi et al. Besides, we announce several enhanced results, power measure function. Particularly, give complete study quadratic form relates work Serre.