积分函数的交换法则
Interchange Rules for Integral Functions
AI总结：
本文提出映射空间中下确界化与积分交换的抽象原理及新条件，统一并改进了积分函数在共轭、次微分、回收、Moreau包络和邻近算子上的交换法则。
摘要：
我们首先提出一个抽象原理，用于在取值于拓扑空间的映射空间上交换下确界化与积分。随后引入关于底层空间和被积函数的新条件，将该原理转化为具体情形，并证明这些情形涵盖了各种现有交换法则的情形。利用这些结果，通过将相应运算移至积分号下，我们改进了在计算积分函数的 Legendre 共轭、次微分、回收锥、Moreau 包络及邻近算子方面的最先进交换法则。
英文摘要：
We first present an abstract principle for the interchange of infimization and integration over spaces of mappings taking values in topological spaces. New conditions on the underlying space and the integrand are then introduced to convert this principle into concrete scenarios that are shown to capture those of various existing interchange rules. These results are leveraged to improve state-of-the-art interchange rules for evaluating Legendre conjugates, subdifferentials, recessions, Moreau envelopes, and proximity operators of integral functions by bringing the corresponding operations under the integral sign.
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。
