In distribution theory the seminorms that you use there $p_m( \phi) := \max_{|\alpha| \le m} \sup_{x \in \Omega} |(\partial^{\alpha}(\phi) (x)|, \phi \in C_c^{\infty}(\Omega)$. Those guys are norms and not just seminorms, right?- I am just wondering because I have a book that keeps on calling them seminorms, so I just wanted to be sure that I am not making a stupid error over and over again
2026-04-03 05:47:10.1775195230
Seminorms in distribution theory are norms, right?
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Yes, they are norms. My guess is that the book calls them semi-norms because the topology in a locally convex topological vector space is defined through a family of semi-norms (which may or may not be norms.)