Density Property of Certain Sets and Their Applications
نویسنده
چکیده
Abstract. In this paper we show that certain sets are dense in R. We give some applications. For example, we show an analytical proof that q 1 n , q is a prime number and e; are irrational numbers. As another application we show: If f is an locally integrable function on R−{0} satisfying ∫ px x f(t)dt and ∫ qx x f(t)dt are constant with ln p ln q is an irrational number; implies f(t) = c t a.e., where c is constant; which is already considered in [1] for the case when f is continuous.
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