Let $(X,\Omega,\mu)$ be a measure space and let $f$ be an extended real valued measurable function defined on $X$. I want help in showing that $$ \mu\left(\{x\in X : |f(x)|\geq t\}\right) \leq \frac{1}{t^2}\int_X f^2~d\mu$$ for any real number $t\gt 0$.
An Application of Chebyshev's inequality?
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real-analysis
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0Are you allowed to use Chebyshev's inequality to prove that? What do you mean by application? – 2012-04-05