AI 中文总结
本文研究α不可预测函数的积分性质，证明积分有界时任意理论泛函回归对积分具有不变性，完善了回归函数积分不变性的相关研究。
AI 中文摘要
本文致力于研究α不可预测函数的积分性质。积分下的回归不变性问题是函数理论中最具挑战性和趣味性的问题之一。我们从周期性开始探讨，随后该问题已针对拟周期函数、殆周期函数及泊松稳定函数得到解决，所有这些问题均受积分有界的条件约束。α不可预测函数是回归函数序列的终点，该类函数是序列元素所呈现的动力学中从规则性到混沌的跨界点。本研究最终证明：若积分结果有界，则任意理论泛函回归对积分具有不变性。
英文摘要
The present paper is devoted to the study of integral properties of alpha unpredictable functions. The problem of invariance of recurrence under integration is one of the most challenging and interesting in the theory of functions. Let us start with periodicity. Next, the problem was solved for quasiperiodic, almost periodic, and Poisson stable functions. All of the problems were subjected to the condition of bounded integrals. The alpha-unpredictable functions are the endpoint in the row of recurrent functions. The class is the cross-border point from regularity to chaos in the dynamics presented through the elements of the row. In the present research, we finalized the proof that any theoretical functional recurrence is invariant with respect to integration, provided the result is bounded.
