Before revision: Following Curry and Kashiwara Schapira seminal works on adapting persistence theory ideas to sheaves on a real vector space in the derived setting , we extensively study their convolution distance on the category of constructible sheavesover the real line D^b_{\mathbb{R .
After revision: Following Curry and Kashiwara Schapira seminal works on adapting persistence theory ideas to sheaves on a real vector space in the derived setting by Kashiwara and Schapira, after J. Curry has made the first link between persistent homology and sheaves .