Extensions of real regular mappings and the Łojasiewicz exponent at infinity

Let V⊂Rn be an algebraic set of positive dimension and let L∞(F) be the Łojasiewicz exponent at infinity of a regular mapping F:V→Rm. We prove that F has a polynomial extension G:Rn→Rm such that L∞(G)=L∞(F). Moreover, we give an estimate of the degree of this extension. Additionally, we prove that if , then for any β∈Q, β