It's my first time to learn measure theory. it's hard for me. Can you guys give me an idea for this problem? thx.
the problem is :
let $f\in L^1(\mathbb{R}^n)$ and define $$f_k(x)= \begin{cases} f(x)&\text{if $|f(x)|\le k$ and $|x|\le k$,}\\ 0 &\text{otherwise}. \end{cases} $$ then, how can I prove that : $\lim_{k\to\infty} \int f_k\, d\lambda = \int f\, d\lambda$
Measurable Function problem
2
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real-analysis
measure-theory
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3Hint: try to find a way to use dominated convergence theorem. – 2012-05-06