Understanding the Impact of Illiquidity on Equivalent Martingale Measures (EMMs) in a Simple Market

I'm currently studying a simple market model with an asset $S$ whose price follows a geometric Brownian motion ( $dS_t=S_t(μdt+σdW_t)$ ) and a risk-free asset $B$ ( $dB_t=B_trdt$ ) over a finite horizon $T$ . I'm trying to understand the impact of illiquidity on the set of Equivalent Martingale Measures (EMMs). In my model, illiquidity is characterized by a constraint on the set of admissible strategies $A$ which becomes $A^*=$ { $(a_t,b_t)∈A:dV_u=a_udS_u+b_udB_u=0$ , $ ∀u∈[t_1,t_2]$ }. This ess