The contributions that make up the main body of the text are devoted to the value of the first order of singular optimization problems, weak convergence in metric spaces, mappings with upper integral
bounds forp-moduli, and many other subjects related to nonlinear analysis and optimization.
In this case, instead of the exactly defined integral E[[a.bar]], we have a lower integral [E.bar][[a.bar]] and an upper integral [bar.E][[a.bar]].
The supremum--which is known to be smaller than or equal to the desired integral [integral] f (x) dx--is called the lower integral, and ther infimum--which is known to be larger than or equal to the desired integral [integral] f (x) dx--is called the upper integral.
Note that the upper integral
limit for 6m in (2) of the present paper is different from that in (3.114) on p.83 of reference .