A question from a rookie on MO.

During my research, I introduced in my physico-mathematical equations some "nasty", "problematic" mathematical objects (namely functional integrals) that are at least **formally/symbolically** defined but way beyond my level of understanding.

- Perhaps they are already (well) known in theory $X$ as object $Y$;
- Perhaps they are unidentified mathematical objects up to now;
- Perhaps they do not make sense;

This I would like to know.

Those objects arise in a seemingly violent collision between dynamical system theory and Bayesian probability theory. Please have a look to question:

**By definition, if I were able to (well) define them, there would be no question at all.**

Since my objects are functional integrals, you can think for instance about Feynman's path integrals to illustrate the situation: brand new mathematical objects only **formally/symbolically** defined at the beginning, takes time to make them well-defined.

So I've submitted one more question on MO, namely

https://mathoverflow.net/questions/237084/sums-series-integrals-whats-next

where:

I explicitly ask about the definition, the existence or the non-existence of my

**formally/symbolically**defined hypothetical mathematical objects in some theory I unfortunately do not know;I provide links to other MO questions where those hypothetical mathematical objects naturally arise, in order to show they do not come from out of space;

But I finally only get comments like:

*Is it well-defined? No. Why not? Because you haven't defined it --- nor even given a hint as to what you mean or what properties such an integral should have.**What properties do you want this operation to have? If you have a set of desiderata, they should be included in the question. If you don't, then of course the answer is that it's easy to define the operation any way you like (might as well take it to be identically zero, for example), and it's also easy to see that this question doesn't belong here

**What if Feynman would ask about his freshly introduced path integral on MO today?**

**Is it well defined? No.**

**Why not? Because you haven't defined it**

**Yes I know, but at least it is symbolically defined!**

**How to escape this vicious circle? At which point Feynman's path integral was sufficiently well/ill defined to deserve consideration from mathematicians?**

So please, how should I reformulate my question in order to get answers like "your object are in fact already known as $Y$ in theory $X$" instead?

FYI, I've asked the same question on SE:

https://math.stackexchange.com/questions/1753921/we-have-sums-series-and-integrals-whats-next

and here I get more constructive answers like:

*Possibly functional integrals or (in QM) path integrals*

It should be the converse, I guess. What's wrong?

Thanks for your help.

Sums, series, integrals. What's next?where I give the "concrete" example of the hypothetical sums/means over "Beth2 terms" (I know that's a serious abuse of terminology) I have in mind: "functional mean images" that are symbolically defined in mathoverflow.net/questions/232043/…. I can't see the link with the Haar measures you mention, but if they are supposed to be related, I'd like to know. $\endgroup$ – Fabrice Pautot Apr 25 '16 at 8:25