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Suppose that there exists a sequence of such that (2.5).
Then there exists a sequence of positive numbers with, for.
Then there exists a sequence of diffeomorphisms fk converging to f in the Sobolev Orlicz space W1,Φ Ω,R2).
By Lemma 2.1, there exists a sequence of points, and such that (3.1).
In fact, for any, there exists a sequence of step functions such that and a.e.
By the same argument as above, there exists a sequence of points such that, and.
Moreover, from assumption, there exists a sequence of elements such that.
Suppose that, then there exists a sequence of natural numbers such that.
Hence, there exists a sequence of paths such that and (3.14).
Under the hypotheses of Lemma 2.7, there exists a sequence of in such that.
We claim that there exists a sequence of points such that.
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