On the comparison of the spaces L1 BV (Rn) and BV (Rn)

The notion of L-1-variation and the space (LBV)-B-1 arise in the study of regularity properties of solutions to perturbed conservation laws. In this article we show that this notion is equivalent to variation in the regular sense, and therefore the space (LBV)-B-1 is the same as the space BV in the sense of Cesari-Tonelli. We also point out some connection between the space (LBV)-B-1 and the Favard classes for translation semigroups.