Large deviations in partial sums of \(U\)-processes in stronger topologies (Q1265960)

Let \(X_i\) be i.i.d. random variables and \(h\) be a measurable and symmetric \({\mathbb R}^d\)-valued function. \(C_m^k\) with \(k,m\in {\mathbb N}\) denotes the set \(\{(i_1, \dots , i_m): 1\leq i_1 < \dots < i_m \leq k \}\). The large deviation principle for partial sums of \(U\)-processes \[ U_n(t)={1\over {n\choose m}} \sum_{C_m^{[nt]}} h(X_{i_1}, \dots , X_{i_m}),\quad t\in [0,1], \] is obtained in a topology, which is an extension of the uniform topology by Orlicz functionals.