Modeling, description, and characterization of fractal pore via mathematical morphology.
We prove that every modular function on a multilattice with values in a topological Abelian group generates a uniformity on which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of .
Conditions, under which the elements of a locally convex vector space are the moments of a regular vector-valued measure and of a Pettis integrable function, both with values in a locally convex vector space, are investigated.
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 ergodic theory, certain sequences of averages may not converge almost everywhere for all f ∈ L¹(X), but a sufficiently rapidly growing subsequence of these averages will be well behaved for all f. The order of growth of this subsequence that is sufficient is often hyperexponential, but not necessarily so. For example, if the averages are , then the subsequence will not be pointwise good even on , but the subsequence will be pointwise good on L¹. Understanding when the hyperexponential...