We show that for any even log-concave probability measure μ \mu on alttext="double-struck upper R Superscript n"> <mml:...

The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed and surface area measures of bodies. We study generalizations these concepts to Borel with density Rn– particular, weighted versions volumes (the so-called measures) when dealing up three distinct then formulate analyze classical measures, obtain a new integral formula for measure As an application, w...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

Suppose two bounded subsets of IR are given. Parametrise the Minkowski combination of these sets by t. The Classical BrunnMinkowski Theorem asserts that the 1/n-th power of the volume of the convex combination is a concave function of t. A Brunn-Minkowski-style theorem is established for another geometric domain functional.

The Brunn-Minkowski type and the cyclic inequalities for i- th general L p -mixed width-integral of convex bodies are established. Further, two differences obtained.

We propose a novel method for the description of spatial patterns formed by a coverage of point sets representing galaxy samples. This method is based on a complete family of morphological measures known as Minkowski functionals, which includes the topological Euler characteristic and geometric descriptors to specify the content, shape and connectivity of spatial sets.