The Relation between the Spaces L1(F ) and L1(T) with Some Applications

Author: Rashad Rashid Haji1&2
1Mathematics Department, College of Education, Salahaddin University, Erbil, Iraq
2Mathematics 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 L1(F),where F={|-N2|+1,|-N2|+2,…,0,…,|N2| is a *finite set for  N > ℕ and the space of Lebesgue integrable functions L1(T), where T=[-π,π] , with some applications by using methods and techniques of nonstandard analysis.

Download the PDF Document from here.

doi: 10.23918/eajse.v4i2p54


C´ızek, V. (1986). Discrete fourier transforms and their applications. Brostol: Adam Hilger Ltd.

Cartier, P., & Perrin, Y. (1995).  Integration over finite sets. In Francine Diener and Marc Diener, editors, Nonstandard analysis in practice, Universitext (pp. 185–204). Springer-Verlag, Berlin.

Cutland, N. (1988). Nonstandard analysis and its applications. London Mathematical Society Student Texts. Cambridge: Cambridge University Press.

Fremlin, D. (2004). Measure theory. Vol. 1. Torres Fremlin, Colchester, The irreducible minimum.

Hurd, A., & Loeb, P. (1985).  An introduction to nonstandard real analysis. Orlando: Academic Press Inc.

Katznelson, Y. (2004). An introduction to harmonic analysis. Cambridge Mathematical Library. Cambridge University Press.

Lak, R. (2015).  Harmonic analysis using methods in Nonstandard analysis. PhD thesis, University of Birmingham, UK.

Ponstein, J. (2002). Nonstandard analysis. University of Groningen, SOM Research School, Groningen. Retrieved from

Robinson, A. (1996).  Non-standard analysis. Princeton Landmarks in Mathematics. Princeton University Press, Princeton, NJ, 1996.

Walker, J. (1988). Fourier analysis. New York: Oxford University Press.

Weaver, J. (1989). Theory of discrete and continuous Fourier analysis. A Wiley-Interscience Publication. New York: John Wiley & Sons Inc.