defined by: $$\label{def:socialLearningMeasure}
    \rho_\Lambda^{i,t}(e,c) \propto \sum_{j=1}^N \lambda^t_{ij}\mathds{1}_{\{k_j(e)=c\}},$$ where $\lambda_{ij}^t$ describes the influence of the individual j on the individual i through \[def:socialLearningMat\] at time $t$.

According to , drawing an element $(e,k_i^t(e))$ using the probability measure $\rho_\Lambda^{i,t}$ is equivalent to randomly drawing an individual $i$ weighted by the coefficient $(\lambda^t_{ij})_{1 \leq j \leq N}$, and randomly choosing an experience $e$ in $\mathcal{E}$.

The probability measure $\rho_{\mathcal{I}}^{i,t}$ representing *individual learning* is given by $$\label{def:individualLearningMeasure}
        \left \{ \begin{aligned}
            & \int_{c \in C} \rho_{\mathcal{I}}^{i,t}(e,c) \, \mathrm{d}c \propto \int_{e' \in E} \mathds{1}_{\{k_i^t(e') \neq 0\}} \mathds{1}_{\{e \in E\}} \exp{-\frac{\|e - e'\|^2}{2 \sigma_E^2}} \, \mathrm{d}e', \\
            & \rho_{\mathcal{I}}^{i,t}(c|e) \propto \mathds{1}_{\{c\in C\}} \exp{-\frac{\|c - f_i^t(e)\|^2}{2 \sigma_C^2}},
        \end{aligned} \right.$$ where $\rho(c|e)$ denotes the conditional probability measure on $\mathcal{C}$, defined for every $(e,c) \in \mathcal E \times \mathcal C$, and every integrable function $\phi$ by $$\int_{\mathcal{E}\times \mathcal{C}}\phi(e,c) \, \mathrm{d}\rho = \int_{\mathcal{E}}\left(\int_{\mathcal{C}}\phi(e,c) \, \mathrm{d}\rho(c|e)\right) \, \mathrm{d}\rho_\mathcal E.$$ In this last expression, $\rho_\mathcal{E} $ denotes the *marginal* probability measure on $\mathcal{E}$, namely $$\rho_\mathcal{E}(e) := \rho(\pi^{-1}(e)), \quad \forall e\in \mathcal{E},$$ where $\pi : \mathcal{E} \times \mathcal{C} \to \mathcal{E}$ is the projection on $\mathcal{E}$.

The individual learning phase is then equivalent for each individual $i$ to draw an element $e'$ experienced by $i$ 