Sentence examples for standard facts from inspiring English sources

First, let us recall some definitions and standard facts about the cone.

In this paper, we use standard facts and notation from Banach spaces and approximation theory.

Now let us recall some definitions and standard facts about the cone.

In this section, we recall some standard facts on A-proper mappings and Fredholm operators.

Now we recall some standard facts on cone theory in Banach spaces.

We refer to [7, 8] for standard facts concerning von Neumann algebras and [9, 10] for noncommutative integration.

It is also a standard fact, "Hardy's convexity theorem", see e.g. [16, Page 9], that (vin mathrm{SH}(D)).

A closely related standard fact is that the continuous spectrum of ( - Delta _g ) is equal to ( [ (frac{n}{2})^2, infty ) ).

A standard fact from dynamical systems with symmetries is that fixed-point subspaces are flow-invariant (cf. [21]), and this fact can be checked directly for (2).

It is a standard fact in group theory (see for instance [25, Proposition 2.4.4]) that if there is a central subgroup of finite index in (G) then the commutator subgroup (G^{prime }) is finite.

Eric Bates, the magazine's editor, said during an interview on MSNBC's "Morning Joe" that McChrystal saw the piece prior to its publication as part of Rolling Stone's standard fact-checking process - and that the general did not object to or dispute any of the reporting.