$d(f,g)=\int_0^1\min\{|f(x)-g(x)|, 1\} dx$, where $f,g$ are measurable, real valued

With the above metric, how can I show that if $(f_n)$ is d-Cauchy iff $(f_n)$ is Cauchy in measure?

Not sure how to start really. I know that $(f_n)$ Cauchy in measure means that $m\{|f_n-f_m|\geq \epsilon \}<\epsilon$ for $m,n$ sufficiently large for any $\epsilon$...


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.