Pseudo-L~p space and convergence

摘要

In the framework of the pseudo-analysis the classical L~p space is generalized and there are proved important properties of introduced space. Three types of convergence of sequences of measurable functions are considered in this space. The inequalities for integrals based on pseudo-integral have been recently proposed as the Holder, Minkowski and Markov inequalities, which are applied in observing relationship among introduced convergences.