Abstract
In this articles we will study the integration of the vectorial functions in Fréchet spaces. Particularly we will introduce and we will study a new functional space and we will prove some theorems of representation.
Highlights
In this articles we will study the integration of the vectorial functions in Frechet spaces
Let the topology of a locally convex space F be defined by a countable number of semi-norms pn (x), with n = 1, 2
Let F be a complex Frechet space and let I be an interval in R; a function f : I → F is simple if it is of the form
Summary
Let the topology of a locally convex space F be defined by a countable number of semi-norms pn (x), with n = 1, 2,. This is the topology of the convergence at each point of X and it is defined by the family of semi-norms of the form. This is the topology of uniform convergence on bounded sets of X and it is defined by the family of semi-norms of the form p (T ) = sup {q (T x)}. L (X, Y) endowed with this topology will be denoted by Lb (X, Y) and it is a locally convex linear topological space. Since any finite set of X is bounded, the simple convergence topology is weaker than the bounded convergence topology
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