The attainment set of the $\varphi$-envelope and genericity properties


  • A. Cabot
  • A. Jourani
  • L. Thibault
  • D. Zagrodny



The attainment set of the $\varphi$-envelope of a function at a given point is investigated. The inclusion of the attainment set of the $\varphi$-envelope of the closed convex hull of a function into the attainment set of the function is preserved in sufficiently general settings to encompass the case $\varphi$ being a norm in a power not less than $1$. The non-emptiness of the attainment set is guaranteed on generic subsets of a given space, in several fundamental cases.


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How to Cite

Cabot, A., Jourani, A., Thibault, L., & Zagrodny, D. (2019). The attainment set of the $\varphi$-envelope and genericity properties. MATHEMATICA SCANDINAVICA, 124(2), 203–246.