f_n measurable

Prove lim inf f_n is measurable?

There's supposedly a proof in Royden'sReal Analysis, but unfortunately I do not have access to it.

Anyone?

Much appreciated.

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- May 13th 2010, 04:37 PMrodlProve limit inferior (lim inf) is measurable?
f_n measurable

Prove lim inf f_n is measurable?

There's supposedly a proof in Royden's*Real Analysis*, but unfortunately I do not have access to it.

Anyone?

Much appreciated. - May 14th 2010, 05:03 AMIdealconvergence
for all a in R, {x in E: limsup{f_n: n in N}(x)>a},

={x in E: limsup{f_n(x): n in N}>a}

= Union {x in E: f_n(x) > a}

= a measurable set - May 14th 2010, 05:13 AMrodl
- May 14th 2010, 08:44 AMrodl
omg.

lim inf f_n = -lim sup (-f_n)

(Clapping)