Weak Derivatives of Functions of Two Variables of Finite Variation

In the paper, we characterize functions of two variables of finite variation with the aid of their weak σ -additive derivatives. The obtained result is an extension of a characterization of absolutely continuous functions of two variables with the aid of their weak integrable derivatives, derived in (Suryanarayana MB, A Sobolev space and a Darboux problem. Pacific J Math 69(2):535–550, 1977).