Quantum anti-Zeno paradox

We establish an exact differential equation for the operator describing tim e-dependent measurements continuous in time and obtain a series solution. S uppose the projection operator E(t) = U(t)EU+(t) is measured continuously f rom t = 0 to T, where E is a projector leaving the initial state unchanged and L(t) a unitary operator obeying U(0) = 1. We prove that the probability of always finding E(t) = 1 from t = 0 to T is unity. If U(t) not equal 1, the watched kettle is sure to "boil.".