Some improvements of convergence rate estimates in the central limit theorem

Four theorems on the rate of convergence in the central limit theorem are formulated in the paper. Theorems 1 and 2 deal with estimates in the case of independent not necessarily identically distributed real random variables (r. v.), theorem 3 – in the case of independent identically distributed (i. i. d.) $R^k$-valued r. v., theorem 4 – in the case of i. i. d. Hilbert space valued r. v. These theorems improve some known results in [2]–[8]. The proofs will be published elsewhere.