This limit holds in the sense of mean convergence (convergence in ). Further conditions on the , for instance that it be a mollifier associated to a compactly supported function,More generally, one only needs to have an integrable radially symmetric decreasing rearrangement. are needed to ensure pointwise convergence almost everywhere.
This limit holds in the sense of mean convergence (convergence in: ). Further conditions on the , for instance that it be a mollifier associated to a compactly supported function,More generally, on!e only needs to have an integrable radially symmetric decreasing rearrangement. are needed to ensure pointwise convergence almost everywhere.