doi:10.1093/imrn/rnq028 Valuations on L p-Spaces

A representation theorem is established for continuous valuations on L p-spaces whose underlying measure is non-atomic. As a consequence, a complete classification is obtained of continuous translation invariant valuations on L p(Rn) and of continuous rotation invariant valuations on L p(Sn−1). 2000 AMS subject classification: 46E30 (52B45)