(c the mapping is continuous, for each.
f ( t, ⋅ ) : B h → H is continuous for each t ∈ J ; 3.
Hence, we have S is continuous since β i is continuous for each i.
If, in addition, the mapping is continuous for each fixed, then is linear.
We note that is continuous for each and is rd-continuous for each.
It is clear that Λf is continuous for each t ∈ R +, whence Λ f ∈ BC ( R +, X ).
Hence, on account of (3.7) and (3.9), it follows that the pair ( T n, I ) is subcompatible for each n ∈ N. Since I and T are continuous, for each n ∈ N, the pair ( T n, I ) is reciprocally continuous.
The operator functions (mathcal{G}) and (mathcal{T}) are strongly continuous, that is, the functions (tin[0,a] to mathcal{G}(t)x) and (tin[0,a] tomathcal{T}(t)x) are continuous for each (x in E).
end{aligned} (2.4) (2) The operator functions (mathcal{G}) and (mathcal{T}) are strongly continuous, that is, the functions (tin[0,a] to mathcal{G}(t)x) and (tin[0,a] tomathcal{T}(t)x) are continuous for each (x in E). .
Furthermore, there exists a θ t invariant set Ω ′ ⊂ Ω of full ℙ measure such that: (1) the mappings t → z i ( θ t ω ), i = 1, 2, are continuous for each ω ∈ Ω ′ ; (2) the random variables ∥ z i ∥, i = 1, 2, are tempered. . the mappings t → z i ( θ t ω ), i = 1, 2, are continuous for each ω ∈ Ω ′ ; the random variables ∥ z i ∥, i = 1, 2, are tempered.
(ii) is continuous for almost each.
