We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A\leq C\leq B$ for standardized $n$-variate functions $A,B$ and discuss the method for constructing this function. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A\leq C\leq B$.

翻译：本文讨论了半相依函数与标准化函数（即满足在点(1,1,…,1)处取值为1的归零化1-递增函数）的避免必然损失及相干性结果。我们刻画了在标准化n元函数A与B约束下，满足A ≤ C ≤ B的k-递增n元函数C的存在性，并探讨了该函数的构造方法。证明过程还涉及将可数无穷网格上的函数延拓至单位超立方体上的函数方法。我们给出了当A（或B）分别等于满足A ≤ C ≤ B的所有k-递增n元函数C集合的逐点下确界（或上确界）时的刻画条件。