For a given sequence of measures μn on the circle T weakly convergent to the Dirac measure, we ask, is it possible to extract a subsequence n(j) such that for any f in the space L1(L2,L∞) the convolutions f * μn(j) converge to f almost everywhere. We show that it is crucial whether the measures are absolutely continuous, discrete or singular (non-atomic).
|Number of pages||12|
|Journal||Real Analysis Exchange|
|State||Published - 2004|
- Almost everywhere convergence