Increase of average energy by the process of measurement

A paradox is pointed out and resolved by proving that the average energy E = (H) of a macroscopic system in thermal equilibrium must increase by the measurement of an observable A which does not commute with the Hamiltonian H. The proof follows as a corollary of a more general result, which states that under certain conditions the expectation value (C) of an observable C should increase by the measurement of another observable A, if [A, C] ≠ 0.