SUBSYMMETRIC LINEAR CONTINUOUS FUNCTIONALS ON SPACES OF LEBESGUE INTEGRABLE FUNCTIONS ON THE SEMI-AXIS - Ivasiuk, I. Ya.; Nykorovych, S. I.; Solomko, A. V. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
The work is devoted to the study of subsymmetric continuous linear functionals on real and complex topological vector spaces of Lebesgue integrable functions on the semi-axis. We consider the class of such spaces satisfying some natural conditions. The complete description of the structure of a subsymmetric continuous linear functional defined on an arbitrary representative of this class has been found. Specifically, we show that every such a functional can be represented as an integral of its argument up to multiplication by a constant.