Generalized Kneser superfunction trick (the iterated limit definition)

[JmsNxn]

ps: why do you use the bullet as composition (instead of \circ)?

I use a bullet because I think of it as a product. And it's not exactly the same thing as \( \circ \). The bullet acts as a binding variable; so we bound the variable \( z \) to \( \Omega \). Then, once we've binded it; we can perform group operations (key word group; composition (as said with \( \circ \)) is not necessarily a group).

If I were to write;

\(
\int_b^c f(s,z)\,ds\circ \int_a^b f(s,z) ds\circ z = \int_a^c f(s,z)\,ds\circ z\\
\)

It's not entirely obvious that we are, first of all binding \( z \) to the integral; and second of all that we are in a group structure. The bullet looks more like multiplication; and its a novel symbol in this scenario; so we don't run into a problem with overriding a symbol that we already use a lot.


It's largely an issue with novelty and precision. And trying to hammer home that it means something different than composition; it's composition restricted to a group structure.