Involutivity of truncated microsupports
  Using a result of J-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf $F$ on a real manifold and an integer $k$, if two functions vanish on the truncated microsupport $Ss_k(F)$, then so does their Poisson bracket. 
Masaki Kashiwara, Teresa Monteiro Fernandes, Pierre Schapira