If someone threatening is on my property, can I shoot them?

I heard this story on T.V. about this guy that attempted to rob this guy but the man getting robbed shot his gun in the air to scare them away. A while later one of the robbers came back to get one of his shoes that he left behind. The home owner noticed him on the property, not in the house, but on the property and shot him dead. Is that technically murder, or is it self defense?