Before revision:  We provide a convenient and tractable sufficient condition for performing IPA , which is intricate to obtain because of the very structure of max-stable fields involving pointwise maxima over an infinite number of random functions.
After revision:  We provide a convenient and tractable conditions ensuring the validity of LRM and IPA in the cases of the Brown--Resnick and Smith field, respectively. Obtaining such conditions is intricate owing to the very structure of max-stable fields involving pointwise maxima over an infinite number of random functions.