Timeline for Linear functionals and continuous functions on open intervals

7 events

when toggle format	what		by	license	comment
Jun 15, 2020 at 7:27	history	edited	CommunityBot		Commonmark migration
Jun 23, 2011 at 14:22	comment	added	Pietro Majer		For instance, in $L^p(\Omega)$ with $1\le p < \infty$ your property is true: $u(t)>0$ a.e. if and only if $\int_\Omega uv dt > 0 $ for all $0\neq v\ge 0$ in $L^q(\Omega) $.
Jun 23, 2011 at 12:28	comment	added	ADegorre		@Pietro Majer: thank you very much. So I see, so we can (albeit non-constructively)define a kind of limit even though my functions do not converge on borders. It is actually worse than that, since the kind of functions I consider in my application usually have a limit. What other conditions on the function space could I add to forbid such a counter-example, if you have an idea?
Jun 23, 2011 at 12:13	vote	accept	ADegorre
Jun 23, 2011 at 12:06	history	edited	Pietro Majer	CC BY-SA 3.0	added 70 characters in body
Jun 23, 2011 at 11:54	history	edited	Pietro Majer	CC BY-SA 3.0	added 314 characters in body
Jun 23, 2011 at 11:38	history	answered	Pietro Majer	CC BY-SA 3.0