By assumption, there exists a subnet { x η } of { x γ β } Δ-converging to x.
The gateway node is assumed to communicate earthquake information to other gateway nodes and to decide about the required actions by the actors in a subnet.
We show that network estimates for single pairwise treatment comparisons can be approximated by the evidence of a subnet that is decomposable into independent paths.
The approximation of the network estimate for a single comparison by the evidence of a subnet and the visualisation of the decomposition into independent paths provide the applicability of a graphical validation instrument that is known from classical meta-analysis.
In the following, we show that a single network effect estimate (e.g. for the comparison between treatments A and B) can also be approximated by the evidence of a subnet that is decomposable into independent paths and can be visualised in a forest plot.
mapping with compact values, by Lemma 2.2, there exists a subnet of ({v_{alpha}}), denoted again by ({v_{alpha}}), such that (v_{alpha}rightarrow v_{0}in F(x_{0},y,z_{0})).
Since (F cdot,cdot,cdot)) is u.s.c. with compact values, by Lemma 2.2, there exists a subnet of ({v_{alpha}}), denoted again by ({v_{alpha }}), such that (v_{alpha}rightarrow v_{0}in F(x_{0},y,z)).
Since B is u.s.c. with compact valued, by Lemma 2.2, there exists a subnet of ({z_{alpha}}), denoted again by ({z_{alpha}}), such that (z_{alpha}rightarrow z_{0}in B(x_{0})).
Then by Proposition 2.6, there exists a subnet of such that { T μ α β x } Δ-converges to some x0 ∈ C. By Lemma 3.8, x 0 ∈ F ( S ).
