Hi All;

I need The solution of the following question"

Let $\displaystyle X$ be a set of measurable functions from a measurable set $\displaystyle I$ to $\displaystyle \Re$ , then we defined a metric $\displaystyle d$ on $\displaystyle X$ By

$\displaystyle d(f,g)=\inf_{\varepsilon\longrightarrow0}(\varepsi lon+m(t:|f(t)-g(t)|\geq \varepsilon))$,

Then prove that d is a metric on $\displaystyle X$.