Sentence examples for be an arbitrary integrable from inspiring English sources

(ii) ⇒ (iii): let be an arbitrary integrable martingale difference array.

Let f (t) be an arbitrary real bounded function, which is square integrable in the interval [0,1), and e ( t ) = f ( t ) - f ̂ m ( t ) Open image in new window, t ∈ [0,1), where f ̂ m ( t ) = ∑ i = 1 m f i ϕ i ( t ) Open image in new window, is the block pulse series of f(t). Then, ∥ e ( t ) ∥ 2 ≤ O ( h 2 ). Open image in new window. See [8].

Let be an arbitrary function.

(xiv) Let be an arbitrary.

Let be an arbitrary element.

Let be an arbitrary graph.

end{aligned} (32) Now, suppose that (f(x)) is an arbitrary square-integrable function on the intervals (Omega_{i}) ((i=1,2,ldots,n+1)).

It's an arbitrary number.

A planet is an arbitrary thing.

"But that is an arbitrary definition.

Admittedly, that was an arbitrary figure.