A more "complete picture" of the relationship between various modes of convergence I am trying to generate/looking for a more comprehensive/complete list/diagram of how the 4 major modes (as listed on wikipedia) of convergence of random variables relate to each other:


*

*Distribution (law)

*Probability

*Almost sure

*$\mathcal{L}^p$ (in mean)


Wikipedia also has this handy little chart (image versions of this exist online as well)
$$\begin{matrix}
  \xrightarrow{L^s}  & \underset{s>r\geq1}{\Rightarrow} &  \xrightarrow{L^r}  &             & \\
                     &                                  &     \Downarrow     &             & \\
  \xrightarrow{a.s.} &            \Rightarrow           & \xrightarrow{\ p\ } & \Rightarrow & \xrightarrow{\ d\ }
  \end{matrix}$$
What I am trying to generate/looking for is something like this:
$$
\begin{matrix}
  \xrightarrow{L^s}  & \underset{s>r\geq1}{\Rightarrow} &  \xrightarrow{L^r}  &             & \\
                   &                                  &     \Downarrow \overset{(a)}{\uparrow}     &             & \\
  \xrightarrow{a.s.} &           \underset{\overset{(b)}{\leftarrow}}{\Rightarrow}           & \xrightarrow{\ p\ } & \Rightarrow & \xrightarrow{\ d\ }
  \end{matrix}$$
Where: $(a) = $ "with uniform integrability" and $(b) = \text{ if } \forall \epsilon> 0, \sum_n \mathbb{P} \left(|X_n - X| > \varepsilon\right) < \infty$
and so on and so forth. Does anyone know if anything like this exists? Does anyone want to help me fill this out? Can anyone suggest a better format for organizing this? 
Thanks!
 A: Gearoid de Barra's 2003 book Measure Theory and Integration contains an entire section called "Convergence Diagrams" (7.3, pp.128-131) concerning six modes of convergence in three different settings: almost everywhere, in mean, uniform, in $L^p$, almost uniform, and in measure. The settings are: the general case, the case where $\mu(X) < \infty$, and the case where the sequence of converging functions is dominated by an $L^1$ function. In each setting, the diagram features arrows between modes of convergence: an arrow from mode 1 to mode 2 means, in that setting, convergence in mode 1 implies convergence in mode 2. For example, in the general case, almost uniform convergence implies almost everywhere convergence; if the space has finite measure, the converse is true, and the arrow is there to show this. 
The subsequent section devoted to counterexamples illustrating the non-implications between the modes, which explain why the diagrams lack arrows where they do. Some of the relevant pages are visible on Google Books.
