Let $0\leq s_1\leq\cdots\leq s_n$ and $0\leq t_1\leq\dots\leq t_n$ be real numbers such that$$\sum_{i=1}^n s_i = \sum_{i=1}^n t_i\; \mbox{and} \;\; \sum_{i=1}^k s_i \leq \sum_{i=1}^k t_i\;\; (k=1,\dots,n-1$$ Then for any nonnegative numbers $x_1,\dots,x_n$ ,$$\sum_\sigma x_1^{s_{\sigma(1)}}\dots x_n^{s_{\sigma(n)}} \geq \sum_\sigma x_1^{t_{\sigma(1)}}\dots x_n^{t_{\sigma(n)}$$ where the sums run over all permutations $\sigma$ of $\{1,2,\dots,n\}$ .