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We present a characterization of inclusion among Riesz−Medvedev bounded variation spaces, i.e., we shall present necessary and sufficient conditions for the Young functions ${\varphi }_1$ and ${\varphi }_2$ so that $R{V}_{{\varphi }_1}[a,b]\subset R{V}_{\varphi {}_2}[a,b]$ or $R{V}_{{\varphi }_1}^{*}[a,b]\subset R{V}_{{\varphi }_2}^{*}[a,b]$.

This paper is devoted to discuss some generalizations of the bounded total $\Phi$-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total $\Phi$-variation in Schramm sense has the structure of a Banach algebra.