Tuesday, August 13, 2019

real analysis - How to find $lim_{n rightarrow infty } sqrt[n]{ int_0^1 |f(x)|^{n} dx } $?

How to find $\lim_{n \rightarrow \infty } \sqrt[n]{ \int_0^1 |f(x)|^{n} dx } $ , where $f(x)$ is a continuous real function on $[0,1]$?

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analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...