In this paper, we investigate to what extent the conclusion of the Lebesgue dominated convergence theorem holds if the assumption of dominance is dropped. Specifically, we study both topological and algebraic genericity of the family of all null sequences of functions that, being continuous on a locally compact space and integrable with respect to a given Borel measure in it, are not controlled by an integrable function.

中文翻译：

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可积分函数的非支配序列

在本文中，我们研究了如果放弃支配地位的假设，则在多大程度上保留了勒贝格主导的收敛定理的结论。具体来说，我们研究了函数的所有空序列族的拓扑和代数通用性，这些函数在局部紧空间上是连续的，并且相对于其中的给定Borel度量是可积的，不受可积函数的控制。