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Please prove lemma 3

Values of the Random Variable
and \( |A, A| \mid=\varepsilon(\delta \neq 0, \varepsilon>0) \). the cigenalues \( \lambda, i=x+1, \ldots, n \) may be clase to zero for a sufficiently small e. Then \( \tilde{g}:=\tilde{y}_{i} / \lambda \) may be large for small perturbations of \( A_{n} \) and \( y_{\mathrm{I}} \). This implies that the soturion of the system of linear equations \( A g=\nu \) is unstable. The regularization method proposed in Tikhonov and Arsenin (1977) involves the stabilization of solutions using the reduction of the set of possible solutions \( D \subseteq U \) to a compact set \( D^{\prime} \) due to the following lemma. Lemma 3 The inverse operator \( A^{-1} \) is continuous on the set \( N^{+}=A D^{*} \) if the contimeus, one-to-one operator \( A \) is defined on the compact \( D^{-} \in D \subseteq U \).

Given :) If the continuous one-to-one operator A is defined on the compact D??D?U. Aim :) The inverse operator A?1 is continuous on the set N?=AD?.