His doctorate, under Banach 's supervision, was awarded in 1935. Mazur was a close collaborator with Banach at Lvov and became a member of the Lvov School of Mathematics, a group of about a dozen mathematicians working in functional analysis, real functions and probability theory .
Ang kanyang mga titulo ng doktor, sa ilalim ng Banach 's pangangasiwa, ay iginawad sa 1935. Mazur ay isang malapit na tagatulong sa Banach sa Lvov at naging isang miyembro ng Lvov School of Mathematics, isang grupo ng tungkol sa isang dosenang mga mathematicians nagtatrabaho sa functional analysis, tunay na pag-andar at ng probabilidad theory.