Is there a name for this infinite language?$$L = \{ 0(,1)^*(,2)^*(,3)^*....(,n)^* \;\mid n \geq 1\}$$A string $w \in L$ is simply an ordered list of increasing integers in which every integer  $\geq 1$ can be repeated 0 or more times, for example 0, 0,1, 0,1,2,2, 0,1,2,3, 0,1,1,4,4,4,21,21.Or perhaps a name for its unary variant: $L_U = \{ 1^{x_1}(,1^{x_1})^*,1^{x_2}(,1^{x_2})^*,...,1^{x_n}(,1^{x_n})^* \mid x_1<x_2<...<x_n\}$
Is there a name for this infinite language?
terminology
Non-decreasing sequences of natural numbers.