We study the complexity of high-dimensional approximation in $L_2$-norm when different classes information are available; we compare power function evaluations with arbitrary continuous linear measurements. Here, discuss situation number measurements required to achieve an error $\varepsilon \in (0,1)$ dimension $d\in\mathbb{N}$ depends only poly-logarithmically on $\varepsilon^{-1}$. This corr...

Abstract In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue Khintchine’s theorem for these sets. We then apply to the topic intrinsic Diophantine Approximation on self-similar particular, define new height element $${\mathbb {Q}}^d$$ <mml:m...