Spaces of all entire functions f represented by vector valued Dirichlet series and having slow growth have been considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous transformations is characterized. Proper bases have also been characterized in terms of growth parameters.

The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

Summary Previous Mizar articles [7, 6, 5] formalized the implicit and inverse function theorems for Frechet continuously differentiable maps on Banach spaces. In this paper, using system [1], [2], we formalize these Euclidean spaces by specializing them. We referred to [4], [12], [10], [11] in formalization.