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In this paper we extend the well known Riesz lemma to the class of bounded $\varphi$-variation functions in the sense of Riesz defined on a rectangle $I_a^b\subset {ℝ}^2$. This concept was introduced in [2], where the authors proved that the space $B{V}_{\varphi }^R(I_a^b;ℝ$ of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].