Weak L^p [0,1] L^p [0,1] is lineable - Farokhinia, Ali; Mohammad Ali Nassab, Mohammad Javad (Journal of Global Research in Mathematical Archives(JGRMA), 2014)
Weak L^p spaces are function spaces that are closed to L^p spaces, but somehow larger. The question that we are going to partially answer in this paper, is that how much it is larger. Actually we prove that Weak L^p [0,1] L^p [0,1] {0} contains an infinite dimensional vector space.