in the paper "Economic conditions and the popularity of parties: a survey" Kirchgaessner (1986) transforms a utility function from continuous to discrete. I get the intuition and the meaning, I just do not get, where the (1-lambda) in front of the sum in [2.4] comes from, when transforming the integral [2.3] to a sum [2.4]. Can anyone help? I attached a picture of both equations. There are no further steps given in the paper.
Formulas in tex:
GP(t_{l}) = GP(0)exp(-\mu t_{l}) + \int_{0}^{l}g(F(x(t),t))exp(\mu (t-t_{l})) dt \ \ [2.3] \newline
GP_{l} = GP_{0} \lambda^{l} + (1-\lambda) \sum_{t=1}^{l}(g(f(x_{t}),t))\lambda^{l-t} \ \ [2.4] \newline
\lambda := exp(-\mu)
