The lower box dimension $ \underline{\dim}_{B} $ of a metric compactum $ (X,\rho) $ appeared originally in 1932in the work of Pontryagin and Schnirelmann,who proved that $ \underline{\dim}_{B}X $ is always greater than or equal tothe topological dimension $ \dim X $ and each metrizable compactum admits a metricwith $ \underline{\dim}_{B}X=\dim X $ .The present article shows that,given an infinite metrizable compactum $ X $ and a real $ b $ satisfying $ \dim X\leq b\leq\infty $ ,there exists a metric on $ X $ compatible with the topologysuch that $ \underline{\dim}_{B}X=b $ .
