Convergence in Measure Theorems of the Choquet Integral Revisited
Convergence in Measure Theorems of the Choquet Integral Revisited
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DOI：
10.1007/978-3-030-26773-5_2
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发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
J. Kawabe
中科院分区：
文献类型：
--
作者：
J. Kawabe
单调收敛定理、Fatou 和反 Fatou 引理以及可测函数在测度上收敛的 Choquet 积分的主导收敛定理的有效性均由单调自连续性和自连续性的条件版本充分表征。在这些定理中，非加性测度可能是无限的，并且函数可能是无界的。还讨论了对偶测度形式以及对称和非对称 Choquet 积分的推广。
The validity of the monotone convergence theorem, the Fatou and the reverse Fatou lemmas, and the dominated convergence theorem of the Choquet integral of measurable functions converging in measure are fully characterized by the conditional versions of the monotone autocontinuity and the autocontinuity. In those theorems the nonadditive measure may be infinite and the functions may be unbounded. The dual measure forms and the extension to symmetric and asymmetric Choquet integrals are also discussed.