Show that for measurable f ess sup f sup f show that these
If f, g are measurable functions, then ess sup (f + g) ≤ ess sup f + ess sup g.
Show that for measurable f, ess sup f ≤ sup f. Show that these quantities coincide when f is continuous.
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if f g are measurable functions then ess sup f g le ess sup f ess sup gshow that for measurable f ess sup f le sup f
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