monotonicity theorem (theorem 2.2)

[abhishek.padmanabh]

I did not really understand this theorem, could you please help me what principle this is trying to setup? If portfolio A is always least worth as much as B then one can go always go long on A and short B and make money. What is the significance of bring portfolio C in context comprising of (A+B)? Where is the possibility of arbitrage and C having positive value at any t, so as to avoid possibility of making money with zero cost and no risk? Could you please help me understand this from a different angle or point out what I am missing?

[mj]

The result is to say that if A is always worth at least as much as B at some time in the future, and sometimes more, then it is worth more than B today.