A Generalization of Natural Density

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Authors :

R. Vembu a,* and A. Bowrna b

Author Address :

a Department of Mathematics, SBK College, Aruppukottai - 626 101, India.
b Department of Mathematics, Sri Ramanas Arts and Science College for Women, Aruppukottai, India.

*Corresponding author.

Abstract :

The concept of natural density is generalized. It is proved that the new theory is consistent with the existing theory in the literature. Many new results were obtained. A theorem analogous to the Riemann’s theorem on rearrangement of non-absolutely convergent series is proved in the sense of generalized natural density. Some more possible generalizations are suggested.

Keywords :

Natural Density.

DOI :

Article Info :

Received : November 24, 2015; Accepted : April 15, 2016.

 

 

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