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PlotStyle in MultipleListPlot


In the function MultipleListPlot, I am trying to give each plot a 
specified thickness as well as a specific color. I have tried various 
variants of

PlotStyle ->{{Thickness[0.01], RGBColor[1, 0, 0]}, {Thickness[0.02], 
RGBColor[0, 1, 0]}}

but nothing seems to work.
any tips?

-Andrew


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