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We prove a quasiconformal analogue of Koebe's theorem related to the average Jacobian and use a normal family argument here to prove a quasiregular analogue of this result in certain domains inn-dimensional space. As an application, we establish that Lipschitz-type properties are inherited by a quasiregular function from its modulo. We also prove some results of Hardy-Littlewood type for Lipschitz-type spaces in several dimensions, give the characterization of Lipschitz-type spaces fordoi:10.1155/2014/895074 fatcat:rtv4z37drfgv7m3pq7efxqubjy