Looks like powdery mildew to me. I usually start seeing that on squash at this time of year.
I spray a mixture of baking soda and water when I have this problem. It does not kill the mildew, it just changes the pH to an unacceptable level and keeps it from growing. It needs to be re-applied frequently. I think that milk is supposed to act the same way but I do not want to smell sour milk.
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