$f: X\to \mathbb R$ be nontrivial continuous, given the fact that
$\sup \int\limits_df\mu_n<\infty\forall n$, then could anyone tell me whether $\{\mu_n\}$ is a tight sequence of a probability measure on $X$? Thanks for any help.
2026-03-26 06:28:23.1774506503
a condition for a tightness of measure
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If $f=0$ then the hypothesis says nothing and $(\mu_n)$ need not be tight.