an old conjecture of erd\h os and szemer\'edi states that if $a$ is a finite set of integers then the sum-set or the product-set should be large. the sum-set of $a$ is defined as $a+a=\{a+b | a,b \in a\}$ and the product set is $a\cdot a=\{ab | a,b \in a\}.$ erd\h os and szemer\'edi conjectured that the sum-set or the product set is almost quadratic in the size of $a,$ i.e. $\max (|a+a|,|a\cdot a|)\geq c|a|^{2-\delta}$ for any positive $\delta$. i proved earlier that $\max (|a+a|,|a\cdot a|)\geq c|a|^{14/11}/\log{|a|},$ for any finite set of complex numbers, $a.$ in this talk we improve the bound further for sets of real numbers.