A remarkable result of Henson and Ross states that if a function whose graph is Souslin in the product of two hyperfinite sets in an N 1  saturated nonstandard universe possesses a certain nice property (capacity) then there exists an internal subfunction of the given one possessing the same property. In particular, they prove that every 1-1 Souslin function preserves any internal counting measure, and show that every two internal sets A and B with |A|/|B|∼1 are Borel bijective. Here we first show that injective Borel functions map Borel sets into Borel sets, a fact well known in classical descriptive set theory. Then, we extend the result of Henson and Ross concerning the Borel bijectivity of internal sets whose quotient of cardinalities is infinitely closed to 1
['Bosko Zivaljevic']
Some Results About Borel Sets in Descriptive Set Theory of Hyperfinite Sets