Open AccessOn the weakly-* dense subsets in $L^{\infty}(\Omega)$
Author(s) -
Peter I. Kogut,
T.N. Rudyanova
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/240818
Subject(s) - omega , convergence (economics) , mathematics , property (philosophy) , space (punctuation) , set (abstract data type) , variable (mathematics) , pure mathematics , combinatorics , mathematical analysis , physics , computer science , quantum mechanics , philosophy , epistemology , economics , programming language , economic growth , operating system
In this paper we study the density property of the compactly supported smooth functions in the space $L^{\infty}(\Omega)$. We show that this set is dense with respect to the weak-* convergence in variable spaces.