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We present a survey of the Lusin condition (N) for -Sobolev mappings defined in a domain G of . Applications to the boundary behavior of conformal mappings are discussed.
It is shown that the approximate continuity of the dilatation matrix of a quasiregular mapping f at implies the local injectivity and the asymptotic linearity of f at . Sufficient conditions for to behave asymptotically as are given. Some global injectivity results are derived.
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