Assume $$f_n,fin L^2(mathbb{R}^3)$$ and $$f_nto f$$ strongly in $$L^2$$. It appears there’s a frequent incontrovertible fact that there exists a superquadratic maps $$betain C([0,infty);[0,infty))$$ such that $$beta(0)=0$$, $$beta(t)t^{-2}to+infty$$ as $$tto+infty$$, $$beta(t)t^{-1}to+infty$$ as $$tto0^+$$, and $$int_{mathbb{R}^3}beta(f_n),dxle C the place $$C$$ is unbiased of $$n$$. I’ve seen in lots of papers however I am unable to discover it within the textbooks.