I am looking at my modes of convergence of functions in measure theory and I want to include common modes of convergence which arise in functional analysis, measure theory, stochastic analysis and PDEs. So far my list includes:
- Uniform Convergence
- Pointwise Convergence
- Uniform Convergence a.e.
- Pointwise Convergence a.e.
- Convergence in $L^p(\mu)$ for $p\in[1,\infty]$
- Convergence in Measure
- Weak Convergence in a Hilbert Space
I understand that there is also some type of convergence in Hilbert spaces which uses test functions instead of arbitrary functions in the Hilbert space. I am mainly looking for references of other common forms of convergence and their definition, in particular for Stochastic Analysis and if they relate immediately to any other modes of convergence list here or are implied by them.