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This is somehow, related to my last doubt(question), Let $X_n(x_0)$ be a (weak) Feller Markov chain on $[0,1]$, starting from $x_0\in \mathbb [0,1]$. I am given that $ \lim\limits_{n\to \infty}\sum\limits_{k=0}^{n-1}\text{prob}(X_k(x_0)\in K)>0$, where $K$ is a compact subset of $[0,1]$ with $\mu(K)=0$, where $\mu$ is Lebesgue measure. Now could any-one tell me how to show that there is an invariant measure(weak)?[Hint: Portmanteau theorem]. Thanks so much for any little help to proceed!

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    $\begingroup$ Is this a homework question? $\endgroup$ – Anthony Quas Nov 28 at 16:47

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