Convex Analysis (Rockafellar, 1970) -- Chapter 07 -- Section 35 -- Part 20

section Chap07section Section35attribute [local instance] Classical.propDecidableopen scoped Pointwiseopen scoped Topology

The former contents attempted to derive joint local finiteness from singleton coordinate subdifferentials. That implication is false for extended-real saddle kernels: a separately convex-concave checkerboard can be finite on both coordinate axes and infinite off-axis. The downstream differentiability theorem now takes local finiteness as an explicit qualification.

end Section35end Chap07