A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff...

We present a survey of the theory measures noncompactness and discuss some fixed point theorems Darbo’s type. apply technique to characterization classes compact operators between certain sequence spaces, in solving infinite systems integral equations spaces. also recent results related existence best proximity points (pairs) for cyclic noncyclic condensing Banach spaces equipped with suitable ...

In this paper, we study the existence of mild solutions for quasilinear integrodifferential equations with nonlocal conditions in Banach spaces. The results are established by using Hausdorff’s measure of noncompactness.

We fill the gap in understanding the relationship between mappings which are condensing w.r.t. the measure of noncompactness defined on the hyperspace and multifunctions condensing in the ordinary sense.