Definition:Ordering on Multiindices
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Definition
Let $Z$ be the set of multiindices.
We define an ordering on $Z$ as follows.
Let:
- $k = \sequence {k_j}_{j \mathop \in J}$
- $\ell = \sequence {\ell_j}_{j \mathop \in J}$
be multiindices.
Then we write:
- $k \preceq \ell$
- $\paren {\forall j \in J} \paren {k_j \le \ell_j}$
By abuse of notation, it is standard to use $\le$ to denote the ordering on the set of multiindices as well.