Complex sentence: A type of integral he introduced in his dissertation became known as "the Hellinger integral", used for defining the Hellinger distance, and the Hilbert-Hellinger theory of forms in infinitely many variables profoundly influenced mathematical analysis.
Split into simpler sentences: A type of integral which he introduced in his dissertation became known as "the Hellinger integral", used for defining the Hellinger distance. In addition, the Hilbert-Hellinger theory of forms in infinitely many variables profoundly influenced mathematical analysis.