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Jul 6, 2015 at 8:27 comment added Alex M. Thank you, this seems to be exactly what I needed. 1) Could you direct me to a proof, please? 2)Would your result still be valid if $T$ were just linear, but not continuous? I.e. showing that a linear form is in fact a regular distribution. 3) If I wanted "continuous" instead of "locally integrable", could I just replace $L^1$ by the space of continuous functions?
Jun 23, 2015 at 19:33 history edited corserine CC BY-SA 3.0
corrected mistake
Jun 23, 2015 at 18:40 comment added Alex M. Did you mean to say that $x_n$ converges to $0$? Otherwise, I can just take a constant sequence of functions, and I do not think that this is what you meant.
Jun 23, 2015 at 14:15 history answered corserine CC BY-SA 3.0