Abstract
In the present paper we introduce the upper and lower exponential density functions of subsets A ⊆ ℕ*. We identify completely the form of the upper density and find many properties for the lower one. We provide examples and list some open problems.
The authors gratefully acknowledge the financial supports of the University Jean Monnet (Saint-Etienne), of the Italian Research Grant PRIN 2008 Probability and Finance and the French Project CAESAR ANR-12-BS01-0011 (responsible Prof. Alain Plagne).
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