扩散松弛中出现的一种收敛模式
A mode of convergence arising in diffusive relaxation
AI总结：
该研究提出一种可测函数的收敛模式，定义了对应柯西序列并证明其完备性，还探讨了复合下的收敛保持，该模式源自扩散松弛极限相关的流体密度收敛证明研究。
摘要：
本文引入了可测函数的一种收敛模式，给出了相关的柯西序列概念，并证明该收敛概念是完备的，即柯西序列均收敛。此外，本文还研究了复合运算下收敛性的保持情况。这种收敛模式的提出，源于证明Euler系统的密度作为松弛极限下收敛的结果，会（通过子序列）几乎处处收敛于非线性扩散系统密度的研究路径。
英文摘要：
In this work, a mode of convergence for measurable functions is introduced. A related notion of Cauchy sequence is given and it is proved that this notion of convergence is complete in the sense that Cauchy sequences converge. Moreover, the preservation of convergence under composition is investigated. The origin of this mode of convergence lies in the path of proving that the density of a Euler system converges almost everywhere (up to subsequences) towards the density of a non-linear diffusion system, as a consequence of the convergence in the relaxation limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
