Messbare Funktion/Tschebyschow-Abschätzung/Fakt/Beweis

Beweis

Es sei ${}T={\left\{x\in M\mid f(x)\geq a\right\}}$ . Dann ist

{}T\times [0,a]\subseteq S(f)\,,

also

{}a\cdot \mu (T)=(\mu \otimes \lambda ^{1})(T\times [0,a])\leq (\mu \otimes \lambda ^{1})(S(f))=\int _{M}f\,d\mu \,.

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