Weak $L^p [0,1] \backslash L^p [0,1]$ 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 $Weak~L^p [0,1] \backslash L^p [0,1] \cup \{0\}$ contains an infinite dimensional vector space.