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!.
Fatou's lemma and measurable sets
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real-analysis
measure-theory
measurable-sets
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0What does $\liminf A_k$ even mean, since $A_k$ are sets? I thought $\liminf$ was only defined for real number sequences. – 2012-05-06
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2$\liminf A_k = \bigcup_{k=1}^\infty \bigcap_{n=k}^\infty A_n$ – 2012-05-06
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1@StefanHansen Ah, thank you. – 2012-05-06