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Constructing Nonstandard Hulls and Loeb Measures in Internal Set Theories

“…6A nonstandard construction of the Lebesgue measure can also be carried out without using a Loeb measure as an intermediate step. In the axiomatic approach, one method for doing so is developed by Lyantse and Kudryk [23, Appendix A] in the framework of . Another way is implicit in [10] and explicitly presented in [11] in the framework of , a subtheory of and that conservatively extends + Dependent Choice.…”