Generating new ideals using weighted density via modulus functions

In this paper we extend the idea of weighted density of Balcerzak et al. (2015) by using a modulus function and introduce the idea f-density of weight g of subsets of ω≔{0,1,…} (at the same time extending the notion of f-density (Aizpuru et al., 2014)), which we name dgf where g:ω→[0,∞) satisfies g(n)→∞ and n∕g(n)↛0 and f is a modulus function. The aim of this paper is to show that we can get new ideals Zg(f) consisting of sets A⊂ω for which dgf(A)=0 different from all the previously constructed ideals Zg of Balcerzak et al. (2015) and moreover they retain all the nice properties of the ideals Zg.