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1.
Mona Khare Akhilesh Kumar Singh 《Journal of Mathematical Analysis and Applications》2008,344(1):238-252
The aim of this paper is to introduce and investigate the concept of pseudo-atoms of a real-valued function m defined on an effect algebra L; a few examples of pseudo-atoms and atoms are given in the context of null-additive, null-null-additive and pseudo-null-additive functions and also, some fundamental results for pseudo-atoms under the assumption of null-null-additivity are established. The notions of total variation |m|, positive variation m+ and negative variation m− of a real-valued function m on L are studied elaborately and it is proved for a modular measure m (which is of bounded total variation) defined on a D-lattice L that, m is pseudo-atomic (or atomic) if and only if its total variation |m| is pseudo-atomic (or atomic). Finally, a Jordan type decomposition theorem for an extended real-valued function m of bounded total variation defined on an effect algebra L is proved and some properties on decomposed parts of m such as continuity from below, pseudo-atomicity (or atomicity) and being measure, are discussed. A characterization for the function m to be of bounded total variation is established here and used in proving above-mentioned Jordan type decomposition theorem. 相似文献
2.
Let D be a region, {rn}n∈N a sequence of rational functions of degree at most n and let each rn have at most m poles in D, for m∈N fixed. We prove that if {rn}n∈N converges geometrically to a function f on some continuum S⊂D and if the number of zeros of rn in any compact subset of D is of growth o(n) as n→∞, then the sequence {rn}n∈N converges m1-almost uniformly to a meromorphic function in D. This result about meromorphic continuation is used to obtain Picard-type theorems for the value distribution of m1-maximally convergent rational functions, especially in Padé approximation and Chebyshev rational approximation. 相似文献