L-sets and the Pelczynski-Pitt theorem.
A generalization of the Lyapunov convexity theorem is proved for a vector measure with values in a Banach space with unconditional basis, which is q-concave for some q < ∞ and does not contain any isomorphic copy of l₂.
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.