I have the following sentence:
Note that by equation (1.1) for each point x belongs to set A there exists at least 2 points y in set B(x), and we need to make a measurable selection form it so that the set B(x) remains measurable.
First of all, should I use "note that" or just "note"? "for each apple" or just "each apple"? "exists" or "exist"?
Moreover, do I use "it" correcttly? By "it", I wish to refer to "at least 2 bananas"