1. The problem statement, all variables and given/known data My question is just on the definition of L∞. Is L∞=Lp where p=∞, i.e., is a measurable function in L∞ if ∫Alf(x)l∞<∞? 2. Relevant equations *L∞: The space of all bounded measurable functions on [0,1] (bounded except for possibly on a set of measure zero) *A measurable function is said to belong to Lp if ∫Alf(x)lp<∞. 3. The attempt at a solution Looks like it would be true based on the definition of Lp but I am really not sure since Royden only gives the one definition on L∞.