Density property of certain sets and their applications

2016/03/17 by Sahoo, Manas R.
#54F99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.05331

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 ∫_x ^pxf(t)dt and ∫_x ^qxf(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 \citeb1 for the case when f is continuous.

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