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References
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The author would like to thank the referee for pointing out an omission in the original version of Proposition (2.1) as well as improving the proof.
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Duncan, R.D. Convergence of semi-groups associated with continuous additive functionals of a Markov process. Z. Wahrscheinlichkeitstheorie verw Gebiete 24, 195–202 (1972). https://doi.org/10.1007/BF00532530
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DOI: https://doi.org/10.1007/BF00532530