The main influence on the direction that Steinhaus's research would take was none of the major mathematical figures at Göttingen but rather the influence came from Lebesgue . Steinhaus studied Lebesgue 's two major books Leçons sur l'intégration et la recherche des fonctions primitives (1904) and Leçons sur les séries trigonmétriques (1906) around 1912 after completing his doctorate.
Ang pangunahing impluwensiya sa direksyon na Steinhaus ng pananaliksik ay tumagal ay wala ng malalaking numero at matematika Gottingen kundi ang impluwensiya nagmula sa Lebesgue. Steinhaus-aral ng Lebesgue 's dalawang malaking libro Leçons sur l'Integration et la mabini des fonctions primitives (1904) at Leçons sur les serye trigonmétriques (1906) sa paligid ng 1912 matapos makumpleto ang kanyang titulo ng doktor.