EN
For a function $f ∈ L_{loc}^{p}(ℝⁿ)$ the notion of p-mean variation of order 1, $𝖵₁^{p}(f,ℝⁿ)$ is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space $W^{1,p}(ℝⁿ)$ in terms of $𝖵₁^{p}(f,ℝⁿ)$ is directly related to the characterisation of $W^{1,p}(ℝⁿ)$ by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.