Theory of integration constancy

My theory of integration constant says- "Integration of any particular aspect over a significantly long range of the variants tends to be constant".

Trying to give it a mathematical shape:

[Integration(any aspect function)]long range for the variant(s) -> Constant

Example: let us understand this with an example, by taking an real aspect we all understand very well, that is money. Also in terms of most real world case, a key variant is time. So taking money we earn over a long time, say a life span - 

Integration (money I am going to earn) over my life-span = Constant

this means if my earning curve is very steep at young age, either it is going to go down substantially when I am old or I am going to die early.

This constant value can of course vary from people to people. For example, at 33, I am quite certain that the value of the above integration result for me over my life span will be significantly insignificant compared to same calculated for Bill Gates. So does having two different values for Bill and me proves it to be wrong? Not so simple perhaps, may be we should really integrate over a larger number of people, to make the range of variant significantly large. In other words, if we are thinking of total money earned by a number of people over all their lifespan, the number of people being very very high (not just you, me and Bill), so even though individual earning figures vary widely, total again may tend to constant.  

I wish we could have the earning data for say ten million people over their life-span, then randomly divide them into five or ten sets, and then find the total earnings for each set. That could help us to put the theory at a better judgement.  With information systems getting richer and richer across world, I hope someday some clever statiscian or mathematician will be equipped enough with data sufficient for probing and mining and prove (or disapprove) this theory. Alas, till then,  for proving such a nice hypothesis, we have to rely only on empirical observations.

Some more examples,

Integration (breaths you take) over 5 years = Constant (in this case lifespan may be too long, as we seem to breath in and out quite frequently)

Integration (joy and sadness) over the world at any moment = Constant; this means if I am happy at this moment right now, that is at the expense of someone else’s momentary tough time.

And so on.. really ...