Let a and b be real numbers with a < b , Let υ : [ a, b ] → ℝ be continuous and convex. An n-dimensional extension of the inequality \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{1}{{b - a}}\int\limits_a^b {v(x)dx} \leqq \tfrac{{v(a) + v(b)}}{2}$$ \end{document} is given for a large family of convex sets.