Modeling the processes of differentiation and integration (Q1882286)

Let \(A\) be a nonempty set and let \({\mathbf A}=\{A_{1},\cdots,A_{m}\}\) be a partition of \(A\). The author proposes some probabilistic characteristics of partitions of the set \(A\) (form; size; volume) and investigates properties of these characteristics. The density and mathematical expectation of \(z\)-volume are calculated. The processes of differentiation and integration are investigated. Some applications to the balloting problem are proposed.