Determining the closed subinterval

Reference no: EM131851912

Let g₁, g₂,... be continuous functions on (a, b) ⊂ R such that g_n(x) → g(x) uniformly for x in any closed subinterval of (a, b). Let T_n be a consistent estimator of θ ∈ (a, b). Show that g_n(T_n) is consistent for ϑ = g(θ).

Reference no: EM131851912

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