  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 $A\leq C\leq B$.
