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If $f$ is a Lebesgue measurable function on $R^n$, we define $$K(t)=\lambda\{x\in R^n:|f(x)|>t\}.$$ I want to prove that

  1. $\int_0^{\infty}K(t)dt=\int_{R^n} |f(x)|dx$

  2. If $ f\in L^1 (R^n)$, then $$\lim_{s\rightarrow t^-} K(s)=K(t).$$

I have no idea about these two problems.

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