The minimum of the upper convex density of the product of the Cantor set with itself Original Research Article

Let View the MathML sourceC×C be the product of the Middle Third Cantor set with itself. We prove that the minimum of the upper convex density of View the MathML sourceC×C is achieved at the vertex, that is, View the MathML sourceDcs¯(C×C,V)≤Dcs¯(C×C,x),∀x∈C×C, where VV is a vertex of View the MathML sourceC×C.