Let \(\Omega\) be a bounded open subset of \({\mathbb{R}}^ n\), \(n\geq 1\). A vector valued function \(f: {\bar \Omega}\to {\mathbb{R}}^ k\), \(k\geq 1\), is said to be little-Hölder continuous with exponent \(\sigma\) if \[ (1)\quad \lim_{R\to 0^+}\sup_{x,y\in {\bar \Omega}, 0<| x- y| \leq R}| f(x)-f(y)| /| x-y|^{\sigma}=0. \] The author proves that, if \(\Omega\) is regular enough and \(g\in L^ 1(\Omega;{\mathbb{R}}^ k)\) verifies \[ (2)\quad \lim_{R\to 0^+}\sup_{y\in \Omega, 0