INEQUALITIES AND CONVERGENCE RESULTS FOR BIRKHOFF WEAK INTEGRABLE INTERVAL-VALUED FUNCTIONS WITH RESPECT TO MULTISUBMEASURES

Some inequalities and convergence results are obtained for intervalvalued Birkhoff weak integrable functions with respect to interval-valued multisubmeasures. A representation theorem is established, expressing the intervalvalued Birkhoff weak integral in terms of scalar Birkhoff weak integrals of the endpoint functions with respect to the corresponding endpoint submeasures. This representation is then used to derive several interval-valued inequalities and convergence results, highlighting the conditions under which scalar results can be transferred to the interval-valued setting.