In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue’s dominated convergence theorem and some other results related to this theorem. Also we have proved the bicomplex version of Lebesgue-Radon-Nikodym theorem. Finally we have introduced the idea of hyperbolic version of invariant measure.

中文翻译：

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勒贝格支配收敛定理和双曲不变量测度的双复版本

在本文中，我们研究了任意可测空间上的双复值可测函数。我们已经建立了勒贝格主导收敛定理的双复版本以及与该定理相关的一些其他结果。我们还证明了 Lebesgue-Radon-Nikodym 定理的双复版本。最后我们介绍了不变测度的双曲线版本的思想。