Elastic structures such as sweat bands, bandages, athletic supporters, support straps for incontinence devices and the like are often soiled on their first use and become unpleasant to deal with.  The preferred method of dealing with these soiled structures would be to discard them.  In most instances the cost of the elastic structure is such that it is not ordinarily economically practical to discard the elastic structure after a single use. 
The art has long sought after a low cost disposable elastic structure. 
For example, it is a general practice for the manufacturers of absorbent shields for incontinent care to provide a disposable shield to which reuseable support straps are attached.  Attached straps that are disposable with the shield would be highly desirable but this has not heretofore been economically possible. 
Breathability in an elastic structure is seen as being highly desirable.  A breathable elastic bandage would promote healing.  A breathable elastic support structure would be cooler to wear than existing elastic support structures. 
Presently available elastic structures of the type contemplated by this invention are somewhat stiff and often have a harsh and irritating surface texture. 
Presently available elastic structures of the type contemplated by this invention generally have a uniform surface texture and a uniform degree of elasticity throughout the structure.