Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
We consider several versions of limit theorems for lattice group-valued measures, in which both pointwise convergence of the involved measures and the notions of σ-additivity, (s)-boundedness, regularity, are given in the global sense, that is with respect to a common regulator. We present the construction of some kinds of integrals in the vector lattice context and some Vitali and Lebesgue theorems. Successively we prove some other kinds of limit theorems, in which the main properties of the measures are considered in the classical like sense. Finally, we give different types of decomposition theorems for lattice group-valued measures.
Keywords:
Axiomatic convergence, Bochner integral, Brooks-Jewett theorem, convergence in L1, convergence in measure, Dieudonné theorem, dominated convergence theorem, Lattice group, Lebesgue decomposition, Nikodým convergence theorem, optimal integral, Rickart integral, Schur theorem, Sobczyk- Hammer decomposition, Stone Isomorphism technique, ultrafilter measure, uniform integrability, Vitali theorem, Vitali-Hahn-Saks theorem, Yosida-Hewitt decomposition.
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Authors:Bentham Science Books