The Shilkret integral with respect to a completely maxitive capacity is fully determined by possibility distribution. In this paper, we introduce weaker topological form of maxitivity and show that under assumption the still its distribution for functions are sufficiently regular. Motivated large deviations theory, provide Laplace principle integrals characterize certain separation convexity as...

Abstract Let $k\geq 2$ be an integer. We prove that the 2-automatic sequence of odious numbers $\mathcal {O}$ is a k -additive uniqueness set for multiplicative functions: if function f satisfies multivariate Cauchy’s functional equation $f(x_1+x_2+\cdots +x_k)=f(x_1)+f(x_2)+\cdots +f(x_k)$ arbitrary $x_1,\ldots ,x_k\in \mathcal , then identity $f(n)=n$ all $n\in \mathbb {N}$ .