Mas-Collel, Winston and Green's Microeconomic Theory (3rd editions) offers two definitions of the upper contour set:

  1. enter image description here
  2. enter image description here

How can the equivalence between the two definitions be proved?

  • $\begingroup$ But Def M.C.3 is not a definition of the upper contour set; rather, it's a definition of quasiconcavity of a function. $\endgroup$ – Herr K. Feb 26 '19 at 19:57
  • $\begingroup$ Or are you asking about the equivalence between $\{x\in A:f(x)\ge t\}$ and $\{y\in X:y\succsim x\}$? $\endgroup$ – Herr K. Feb 26 '19 at 20:00
  • $\begingroup$ I have updated the question. The definition of upper contour set in M.C.3 is now highlighted. $\endgroup$ – Bruno Schiavo Feb 26 '19 at 21:29
  • $\begingroup$ Have you given the question some thoughts? This is not a particularly difficult proof. $\endgroup$ – Herr K. Feb 26 '19 at 21:33

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