"HEPA filters were originally developed in the 1940s for military use"

. . . as part of the Manhattan Project.  ". . . developed during the Manhattan Project (which produced the world's first atomic bomb) as a way of trapping extremely dangerous, tiny radioactive particles."

That "Continuous sheet of filter medium" is a filter made of fibers, like clothing, towel, blanket or carpet fibers. 

BENEFITS of HEPA FILTERS

>  Long-lasting.
>  Replaceable. 
>  Remove at least 99.97% of airborne particles.
> 

WHO INVENTED THE HEPA FILTER?

Like many other inventions, HEPA filters developed over time: there doesn't appear to be a single inventor who deserves sole credit. Fiber-based air filters were originally developed during the Manhattan Project (which produced the world's first atomic bomb) as a way of trapping extremely dangerous, tiny radioactive particles. After the war, German brothers Klaus and Manfred Hammes began developing relatively inexpensive air filtering systems during the early 1960s to reduce soot particles produced by coal-fired stoves; they went on to found a company called IQAir, which has been a pioneer of air filtering equipment ever since. The first inexpensive, pleated air filter was patented on April 19, 1966 by Kenneth W. De Baun and you can read all about it in his US patent 3,246,457: Pleated Air Filter Cartridge.