20 мая 2011 г. · If (fn)n is equicontinuous in C[0,1] with the uniform norm, and it converges to some f∈C[0,1] pointwise, then it must converge to f uniformly.

10 янв. 2021 г. · I tried to write down the definition of uniform convergence and then arguing that, in particular, since N∈N from uniform convergence works for ...

8 дек. 2013 г. · Pointwise convergence means at every point the sequence of functions has its own speed of convergence (that can be very fast at some points and ...

29 мая 2013 г. · That's not necessary true, standard example is fn(x)=xn for x∈[0,1) and fn(x)=0 otherwise. They converge point-wise to f≡0 but not uniformly.

13 июн. 2017 г. · @Arthur, No. Improving pointwise convergence to uniform convergence occurs only in rare occasions. For instance, Dini's theorem tells that if ...

29 янв. 2016 г. · fn converges pointwise to the function f(x)=0 if 0≤x<1, f(1)=1, but the convergence is not uniform.

2 мая 2017 г. · Pointwise convergence implies uniform convergence under concavity? ... Showing a sequence of convex functions admits a uniformly convergent ...

28 февр. 2016 г. · As for Egorov's theorem, it certainly holds for pointwise convergence to ∞. Just replace fn by arctanfn. The latter sequence converges pointwise ...

13 июл. 2018 г. · If the pointwise convergence is monotone, then a classical theorem of Dini shows the convergence is indeed uniform.

15 авг. 2015 г. · Pointwise convergence does not imply locally uniform convergence. If the domain of the sequence of functions is compact, locally uniform convergence is even ...