Iterates of a product of conditional expectation operators

Let (Ω,F,μ)(Ω,F,μ) be a probability space and let T=P1P2⋯PdT=P1P2⋯Pd be a finite product of conditional expectations with respect to the sub σ  -algebras F1,F2,…,FdF1,F2,…,Fd. We show that for every f∈Lp(μ)f∈Lp(μ), 1