From: knop@math.rutgers.edu (Friedrich Knop)
Newsgroups: sci.math.research
Subject: Re: Do you know a "non-distribution" ?
Date: 22 Sep 1996 16:08:11 -0400

edgar@math.ohio-state.edu (G. A. Edgar) writes:

>In article <51rbfr$5di@h20-hrze.uni-duisburg.de>,
>martin@math.uni-duisburg.de (Silvio Martin) wrote:

>> A distribution is defined as a linear functional on the space
>> of test functions D, which is contineous in the usual topology
>> of D. With little help of the axiom of choice one can conclude
>> that there are linear functionals on D (defined on all of D),
>> which are not contineous. Does anyone out there know an example
>> for such a "non-distribution" ? Some standard literature didn't
>> help...

>Any such example lives only way out there in Axiom of Choice Land.
>Such examples (provably discontinuous in ZF set theory)
>cannot be explicitly written down. [...]

A nice reference is

Wright, J. D. Maitland: Functional analysis for the practical man.
Functional analysis: surveys and recent results (Proc. Conf., Paderborn,
1976), pp. 283--290. North-Holland Math. Studies, Vol. 27; Notas de Mat.,
No. 63, North-Holland, Amsterdam, 1977.

-Friedrich Knop