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Now, since the function μ ( r ) is a modulus of continuity, it cannot tend to zero too rapidly as ε → 0, that is, for instance, if μ ε → 0 as ε → 0, then μ ≡ 0. Therefore ε − n / 2 e − 1 / 4 ε ≤ c 4 μ , ε → 0. for some constant c 4. Taking into account this in (2.12), we obtain | S ( x, ε ) − f ( x ) | ≤ c μ , ε → 0, where the constant c does not depend on ε > 0. □.
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