**The Relation between the Spaces L**^{1}(F ) and L^{1}(T) with Some Applications

**Author: **Rashad Rashid Haji^{1&2}

^{1}Mathematics Department, College of Education, Salahaddin University, Erbil, Iraq

^{2}Mathematics Education Department, Faculty of Education, Ishik University, Erbil, Iraq

**Abstract: **In this research we find the relation between the nonstandard space of Lebesgue integrable functions L^{1}(F),where F={|-^{N}⁄_{2}|+1,|-^{N}⁄_{2}|+2,…,0,…,|^{N}⁄_{2}| is a *finite set for N > ℕ and the space of Lebesgue integrable functions L^{1}(T), where T=[-π,π] , with some applications by using methods and techniques of nonstandard analysis.

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**doi**: 10.23918/eajse.v4i2p54

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