$\forall \epsilon >0, \exists \sigma >0$ such as : $ [\forall A\in F : P(A)<\sigma ]\Rightarrow [\int_A |x| dP $
For every $\epsilon>0$ there exists $\delta>0$ such that $\int_A|f(x)|\mu(dx) < \epsilon$ whenever $\mu(A) < \delta$