Assumptionless consistency of the Lasso

The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The validity of the Lasso procedure has been theoretically established under a variety of complicated-looking assumptions by various authors. This article shows that for the loss function considered in Tibshirani's original paper, the Lasso is consistent under almost no assumptions at all.