Suppose that E is a vector lattice where the ordering and the lattice operations in E are defined pointwise by a countable family $${\mathcal {F}}=\{f_i|i\in {{\mathbf {N}}}\}$$ of positive linear functional of E and Z is a sublattice of E. Based on algebraic and order properties of E we give necessary and sufficient conditions in order Z to be atomic. Especially we show the existence of a basic sequence $$\{b_n\}$$ of extremal points (atoms) of $$Z_+$$ so that for any $$x\in Z_+$$ a unique sequence $$({\widehat{x}}(n))$$ of real components of x with respect to $$\{b_n\}$$ exists so that $$x=\sup \{{\widehat{x}}(n)b_n\;|\;n\in {{\mathbf {N}}}\}$$ and also $$x=sup_{n}\sum _{i=1}^n{\widehat{x}}(i)b_i$$ . These results give an answer to the problem of the existence of basic derivatives in financial markets.