We announce the result that enables one to determine fairly constructive characteristics of a set of points
of full measure on a sphere $L(S^m)$ at which the strong means converge to a given function $f(\cdot)$.
Citation Example:Lasuriya R. A. The characteristics of points of strong summability of the Fourier - Laplace
series for functions from the class $L(S^m)$ in the case of critical indicator // Ukr. Mat. Zh. - 2002. - 54, № 10. - pp. 1437-1439.