I am reading Statistical Estimation and Asymptotic Theory by Ibragimov and Has'minskii and was confused by the following passage: ... and that we have uniformly in $\theta$ belonging to the compact subsets of $\Theta$: $$\underset{|h|>\epsilon}{\inf}\int^{\infty}_{-\infty} |f(x,\theta+h)-f(x,\theta)|dx >0,\epsilon>0. $$
I understand what the statement implies (that there are no "flat regions" with respect to $\theta$), but not the preceding condition. What does the passage mean in using "uniformly"? Does it mean that for compact subsets of $\Theta$, for any $\epsilon$ there exists a $\delta$ such that the above integral is greater than $\delta$?