c-Algebrability of Pathological Sets of Product Integrable Functions

摘要

In this paper we investigate linear algebraic structures in the set of product integrable matrix-valued functions and find $mathfrak{c}$-generated algebras in $L([a,b],{{mathbb{R}}^{nimes n}})ackslash {{L}^{*}}([a,b],{{mathbb{R}}^{nimes n}})$ and $D([a,b],{{mathbb{R}}^{nimes n}})ackslash {{L}}([a,b],{{mathbb{R}}^{nimes n}})$.