Sentence examples for continuous provided that from inspiring English sources
Further, (r_{m}) is symmetric (resp. continuous) provided that m is as well.
Furthermore, all the conjugacies that we construct are locally Hölder continuous provided that the vectors fields are of class C1.
A function is right dense continuous provided that it is continuous at right dense point in and its left-side limits exist at left-dense points in.
Let us recall that, given a partial metric ( X, p ), a mapping f : X → X is continuous provided that f is continuous from ( X, T ( p ) ) into itself.
A function is right-dense continuous provided that it is continuous at each right-dense point (a point where ) and has a left-sided limit at each left-dense point.
A stochastic process (x :mathbb{R} rightarrow L^{p}(mathbb{P},mathbb{H})) is said to be continuous provided that, for any (s inmathbb{R}), lim_{trightarrow s}EbiglVert x t) - x s bigrVert ^{p} = 0. [24].
In the following, given a partial metric space ( X, p ), we will say that a mapping f : X → X is p s -continuous provided that f is continuous from ( X, T ( p s ) ) into itself.
A function is left dense continuous ( -continuous) provided that it is continuous at all left dense points of, and its right side limits exists (being finite) at right dense points of.
A function is called rd-continuous provided that it is continuous at all right-dense points of and its left-sided limit exists (finite) at left-dense points of.
A function is called rd-continuous provided that it is continuous at right-dense points in and its left-sided limits exist at left-dense points in The set of rd-continuous functions will be denoted by.
The function f : T → R is called ld-continuous provided that it is continuous at each left-dense point and has a right-sided limit at each point, write f ∈ C ld ( T ) = C ld ( T, R ).
