On bounded lower Λ-variation

In the paper we introduce the new concept of variation which allows to work in the spaces of functions measurable in the Lebesgue sense. We define the Banach space ΛBV̲[0,1] and we provide some of its basic geometric and topological properties. We also define the useful notion of good representatives of functions generating the suitable equivalence classes from the space ΛBV̲[0,1] and raise the question of their existence as well as their properties. Moreover, we investigate convolution and superposition operators acting in ΛBV̲[0,1] and give some applications to linear differential and nonlinear integral equations.