Continuity of the solution to the $L_p$ Minkowski problem in Gaussian probability space

Abstract: In this paper, it is proved that the weak convergence of the

L_{p}

Guassian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for

p g e q 1

. Moreover, this paper obtains the solution to the Guassian Minkowski problem is continuous with respect to

p

.

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