Sentence examples for some further notation from inspiring English sources

To define (OC) we need some further notation.

To proceed with the exposition of our problem, we need some further notation.

First, we introduce some further notation and definitions that will be used later.

Some further notation is required for the monotone missing data pattern.

The proof requires some technical lemmas and some further notation: For an interior node z ∈ K (T ) ∩ Ω of T, define the star Σ (T ; z ) ≔ { E ∈ E (T ) : z ∈ E } as well as the patch ω (T ; z ) ≔ { T ∈ T : z ∈ T }.

Let us introduce some further notations.

Before stating the main theorem, we must first introduce some further notations.

In Section 2, we introduce some further notations and recall some useful results, which will be used in the later section.

Further notation can be found in Table 10.

Using the further notation O(0_{(d)},C_{(d)})=left{O x: xin (0_{(d)},C_{(d)}) right}, we assume that the random vectors ξ n,n=1,2,… follow the uniform distribution on O(0(d),C (d)), and are independent.

We will work with non-anticipative functionals as defined in (Cont and Fournié 2010, Definition 1), i.e., with a family F=(F t ) t∈[0,T] of maps ( F_{t}:D [0,t], mathbb {R}^{d} mapsto mathbb {R}.) For all further notation and relevant definitions, we refer to (Cont and Fournié 2010, Section 1).