You're not entangled with the measurement, you're entangled with the entire wave despite the inconceivable number of measurements that happen within it. The same way my friends are still my friends despite us being in different places. I won't know instantly if they die or something, but I react differently when I hear about what happens to them than I do with ordinary people. If one of them gets into a car accident outside my light-cone and I'm more sad when I hear about it than about the car accident of a stranger, that doesn't mean that I have a non-local interaction with the car accident.
