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I don't know how can I imply Fatou's lemma for any measurable sets $A_k$

that is..
$\lambda(\liminf A_k)\le\liminf\lambda(A_k)$

how can I prove it?


and is there any example in $R$ of sequence of measurable sets $A_k$ such that $A_k\subset[0,1]$, $lim\lambda(A_k)=1$, but $\liminf A_k=\varnothing$ ?

thx for your help!.

  • 0
    What does $\liminf A_k$ even mean, since $A_k$ are sets? I thought $\liminf$ was only defined for real number sequences.2012-05-06
  • 2
    $\liminf A_k = \bigcup_{k=1}^\infty \bigcap_{n=k}^\infty A_n$2012-05-06
  • 1
    @StefanHansen Ah, thank you.2012-05-06

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