This is an announcement for the paper “On the boundedness of threshold operators in $L_1[0,1]$ with respect to the Haar basis” by Steven J. Dilworth, Smbat Gogyan, Denka Kutzarova and Thomas Schlumprecht. Abstract: We prove a near-unconditionality property for the normalized Haar basis of $L_1[0,1]$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.05732