  Lemma 1 from the paper [N.E. Gretsky, J.M. Ostroy, W.R. Zame,
Subdifferentiability and the duality gap, Positivity 6: 261--274, 2002] asserts
that the value function $v$ of an infinite dimensional linear programming
problem in standard form is lower semicontinuous whenever $v$ is proper and the
involved spaces are normed vector spaces. In this note one shows that this
statement is false even in finite-dimensional spaces, one provides an example
of linear programming problem in Hilbert spaces whose (proper) value function
is not lower semicontinuous (hence it is not subdifferentiable) at any point in
its domain, one shows that the restriction of the value function to its domain
in Kretschmer's gap example is not bounded on any neighborhood of any point of
the domain, and discuss other assertions done in the same paper.
