The character of convergence of the mean to

can be seen from this graph where first 150 iterations of 100 points x=0.01 step 0.01 = 0.99 are plotted on top of each other.

The limited spread (max-min) of each iteration is also visible with such linear choice and size of steps.

I guess this is somehow related to tree functions (which are related to Lambert function) and iterated logarithms. Just to remember always that studying constant is studying Lambert Wo(1)= so generalizations are possible if things are positioned correctly. So far I do not see them, but I see what to read next.

Ivars

can be seen from this graph where first 150 iterations of 100 points x=0.01 step 0.01 = 0.99 are plotted on top of each other.

The limited spread (max-min) of each iteration is also visible with such linear choice and size of steps.

I guess this is somehow related to tree functions (which are related to Lambert function) and iterated logarithms. Just to remember always that studying constant is studying Lambert Wo(1)= so generalizations are possible if things are positioned correctly. So far I do not see them, but I see what to read next.

Ivars