Strongly near-standard functions in Lebesgue's spaces
P. Borde · Bulletin of the Belgian Mathematical Society - Simon Stevin · 1998
The framework of this paper is Internal Set Theory (IST in [6]).Let P be an interval of R N .We give a characterization of functions f ∈ L p (P ) (1 ≤ p < +∞) which are near-standard with respect to the norm of L p (P ) (i.e.We shall find some applications of this result in reaserch of compact sets in Lebesgue's spaces, but also in operator theory because an operator of L p (P ) is compact if, and only if, it transforms any limited function into a near-standard one.