Properties of Cesàro means of negative order and of certain other $T$-means for Fourier series of continuous functions

The main result established in this article is the following.
Let $\alpha$ be an arbitrary negative nonintegral number. Then every continuous function can be changed on a set of arbitrarily small measure so that if $g(x)$ denotes the new function, then the sequence of the $T$-means (corresponding to the method $(C,\alpha)$) of the function $g(x)$ contains a subsequence converging uniformly to the function $g(x)$.
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