Pointwise convergence conjecture for polynomial multilinear ergodic averages
Pointwise convergence conjecture. For every such system, polynomial family, and mmm-tuple f=(f1,…,fm)f=(f_1,\dots,f_m)f=(f1,…,fm) with fj∈L∞(X)f_j\in L^\infty(\mathbb X)fj∈L∞(X) for j∈[m]j\in[m]j∈[m], the limit