Sentence examples for is continuous that from inspiring English sources

Its sample path is continuous, that is, the function t → W ( t ) is almost surely continuous.

(ii) Its sample path is continuous, that is, the function t → W ( t ) is almost surely continuous.

(C) The inclusion map is continuous, that is, there is a constant, such that, for all, where represents the bounded functions from into.  .

We assume for technical reasons that τ is continuous, that is, τ ∈ C 0 ( Ω ¯ 2, R + p × p ). Moreover biological data indicate that τ is not a symmetric function (that is, τ i j ( r, r ¯ ) ≠ τ j i ( r ¯, r ) ), thus no assumption is made about this symmetry unless otherwise stated.

Note that the embedding (L^{p}(Omega)hookrightarrow L^{ q-1 p'}(Omega)) is continuous, that is, Vert u Vert _{(q-1)p'} L^{ q-1 p Vert u Vert _{p} quad text{for all } u in L^{p}(Omega), (4.3) where (c_{1}) is a positive constant.

It was proved by Nussbaum ([23], Lemma 2) that the radius of the spectrum is continuous, that is, if (L, L_{m}: Xrightarrow X) are compact linear operators and (lim_{mrightarrowinfty}|L_{m}- L| = 0), then (lim_{mrightarrowinfty} r(L_{m}) = r(L)).

This means that is continuous at.

We shall prove that is continuous at.

Suppose that is continuous at a point.

Since the mapping is continuous (note that and are continuous), we have that is closed.

(P3) is continuous in, that is, for any given (3.2).