Today the institute seminar of IMM was held. Prof. of ANAS, sen. Res. ass. of “Mathematical Analysis” department, doct. of math. sci. Bandaliyev Rovshan Alifaga oglu gave a talk on “Density of C₀^∞(Ω)  space in variable degree Lebesgue space and analogue of Kolmogorov-Riesz theorem”.
The talk deals with density of C₀^∞(Ω)  space in variable degree Lebesgue space L_p(x)(Ω) for 0 < p(x) < 1, and on Kolmogorov-Riesz theorem about compactness in this space.
The density of finitely differentiable finite functions space in variable degree Lebesgue space L_p(x)(Ω) for the case 0 < p(x) < 1 was also considered.
It was noted that the family of potential type approximation of a unit in this space was constructed and modular type inequality was proved. As an application of the obtained result, the analogue of Kolmogorov-Riesz compactness theorem in variable degree Lebesgue space was find.

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