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Inverse Property of Consistency [closed]

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Given : $\{T_n\}$ is consistent for $\theta$then $P_{\theta}[|T_n - \theta|>\epsilon]\rightarrow 0$ as $n \rightarrow \infty $

By continuity theorem for continuous funtion $\phi()$,we can

$$|\phi(T_n) - \phi(\theta)>\epsilon|$$for $$|T_n-\theta|>\epsilon$$

then how do we write the relation provided below from the above steps

$P_\theta [|\phi(T_n) -\phi(\theta)|>\epsilon]\leq P_\theta[|T_n - \theta|>\epsilon]$


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