From personal experience at Bankers Trust yes I do believe in...

From personal experience at Bankers Trust yes I do believe in it.

The Trading room was the biggest in the Southern Hemisphere and out of the 300 odd traders the technicians and chartists were easily the most successful traders.

You being a mathematician, will no doubt recognise this simple formula but I say keep it simple.

Birkhoff–Khinchin theorem. Let ƒ be measurable, E(|ƒ|) < ∞, and T be a measure-preserving map. Then with probability 1:



where {\displaystyle E(f|{\mathcal {C}})} is the conditional expectation given the σ-algebra {\displaystyle {\mathcal {C}}} of invariant sets of T.

Corollary (Pointwise Ergodic Theorem): In particular, if T is also ergodic, then {\displaystyle {\mathcal {C}}} is the trivial σ-algebra, and thus with probability 1:
{\displaystyle \lim _{n\rightarrow \infty }\;{\frac {1}{n}}\sum _{k=0}^{n-1}f(T^{k}x)=E(f).}
Enjoy!