Sentence examples for most countable points from inspiring English sources

The function F is of bounded variation and right-continuous, therefore it has at most countable points of left discontinuity.

Especially, let. is bounded and almost surely continuously differentiable for all but at most countable points and at these points, and,,, where denote the derivative of.

In particular, Let and. is bounded and almost surely continuous for all but at most countable points and at these points, and exist,, where is an interval, and denote the right-hand and left-hand limits of the function, respectively.

(PC [ Omega ]) = { varphi: ( - infty,0 ] times Omega to R^{n}|varphi ( s^,x ) = varphi ( s,x )) for (s in ( - infty,0 ]), (varphi ( s^,x )) exists for (s in ( - infty,0 ]), (varphi ( s^,x ) = varphi ( s,x )) for all but at most countable points (s in ( - infty,0 ])}.

(PC[J,R^{n}]= {phi: Jrightarrow R^{n} | phi v mbox{ is continuous for all but at most countable points }v in Jmbox{ and}mboxmbox{at these points }vin J, phi v^ mbox{ and }phi v^ mbox{ exist and }phi v) = phi v^), where (phi v^)) and (phi v^)) denote the left-hand and right-hand limits of the function (phi v)) at time v, respectively, and (Jsubset R) is an interval.

denotes the space of piecewise continuous functions with at most countable discontinuous points and at this points are right continuous.

Let (a(t)) be a continuous scalar function with at most countable zero points on J. Then SIDE has at least a strong solution under Theorems 6.4 and 6.6.

We apply again [35], Theorem IV.5.33] stating that if Σ ess ( A ) is at most countable, any point in Σ ( A ) ∖ Σ ess ( A ) is an isolated eigenvalue with finite multiplicity.

(3) Conclusion 2 also applies even if f is allowed to be discontinuous up to an at most countable set of points.  .

Conclusion 2 also applies even if f is allowed to be discontinuous up to an at most countable set of points.

The reason for this rests in the fact that the sort of proof, employed in Lemma 3 below, fails to work without assuming that q* is continuous up to an at most countable set of points, something that is implied in the monotonicity constraint when q turns out to be a scalar.