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Recently, Nagy-To\'okos and Totik-Varga proved an asymptotically sharp$L^{p}$ Bernstein type inequality on union of finitely many intervals. Weextend this inequality to the case when the power $p$ is between $0$ and $1$;such sharp Bernstein type inequality was proved first by Arestov.

Some notes on $L^{p}$ Bernstein inequality when $0