Abstract: A state is said to be Markovian if it fulfil the important condition of saturating the Strong Subadditivity inequality. I will show how the vacuum state of any relativistic QFT is a Markov state when reduced to certain geometric regions of spacetime. For the CFT vacuum, the Markov property is the key ingredient to prove the A theorem (irreversibility of the RG flow in relativistic QFT in d=4 spacetime dimensions) using vacuum entanglement entropy. This extends the entropic proofs of the c and F theorems in dimensions d=2 and d=3, giving a unified picture. I will also comment on the relation of this Markov property with the unitarity bound and holography.