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Density property of certain sets and their applications | | Manas R. Sahoo
; | | Date: |
17 Mar 2016 | | Abstract: | In this paper we show that certain sets are dense in $mathbb{R}$. We give
some applications. For example, we show an analytical proof that
$q^{frac{1}{n}}$, $q$ is a prime number and $e$; is an irrational number. As
another application we show: If $f$ is an locally integrable function on
$mathbb{R}-{0}$ satisfying $int_x ^{px}f(t)dt$ and $int_x ^{qx}f(t)dt$ are
constant with $frac{ln p}{ln q}$ is an irrational number; implies
$f(t)=frac{c}{t},, a.e.$, where $c$ is constant which is already considered
in cite{b1} for the case when $f$ is continuous. | | Source: | arXiv, 1603.5331 | | Services: | Forum | Review | PDF | Favorites | |
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