Mengenwertige Masse und Fortsetzungen.
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.
Let , where is a measurable space, and a topological space. We study inclusions between three classes of extended real-valued functions on which are upper semicontinuous in and satisfy some measurability conditions.
For a sequence of linear maps defined on a Banach space with values in the space of measurable functions on a semifinite measure space, we examine the behavior of its maximal operator at zero.