Let (X, A, ) be a finite measure space. Let be the set of all extended...

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Let (X, A, μ) be a finite measure space. Let be the set of all extended real- valued A-measurable function on X where we identify functions that are equal a.e. on X. Let If - gl 1+f-gl p(f,g) = x² du for f.g. (a) Show that p is a metric on Þ. (b) Show that is complete w.r.t. the metric p. Let (X, A, μ) be a finite measure space. Let be the set of all extended real- valued A-measurable function on X where we identify functions that are equal a.e. on X. Let If - gl 1+f-gl p(f,g) = x² du for f.g. (a) Show that p is a metric on Þ. (b) Show that is complete w.r.t. the metric p.

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