Functional Erd\"os-R\'enyi law of large numbers for nonconventional sums   under weak dependence
  We obtain a functional Erd\H os-R\' enyi law of large numbers for "nonconventional" sums of the form $\Sig_n=\sum_{m=1}^nF(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of exponentially fast $\psi$-mixing random vectors and $F$ is a Borel vector function extendin in several directions our previous result concerning i.i.d. random variables $X_1,X_2,...$. 
Yuri Kifer
math.PR