About Some Monge–Kantovorich Type Norm and Their Applications to the Theory of Fractals

If X is a Hilbert space, one can consider the space cabv(X) of valued measures defined on Borel sets compact metric having bounded variation. On this vector was already introduced Monge–Kantorovich type norm. Our first goal to introduce norm cabv(X), where Banach but not necessarily space. Thus, we here cabvLq([0,1]),(1<q<∞). We obtained some properties and provided examples. Then, used cabvKn(K being R or C) obtain convergence for sequences fractal associated sequence iterated function systems.