c-Algebrability of Pathological Sets of Product Integrable Functions
c-Algebrability of Pathological Sets of Product Integrable Functions
In this paper we investigate linear algebraic structures in the set of product integrable matrix-valued functions and find $\mathfrak{c}$-generated algebras in $L([a,b],{{\mathbb{R}}^{n\times n}})\backslash {{L}^{*}}([a,b],{{\mathbb{R}}^{n\times n}})$ and $D([a,b],{{\mathbb{R}}^{n\times n}})\backslash {{L}}([a,b],{{\mathbb{R}}^{n\times n}})$.