Could someone clarify the definiton of the function given above? I think it means $\omega_f(a)=\bigcap_{m=1}^{\infty}\bigcup_{n=m}^{\infty}\{ |f(x')-f(x'')| : a-\frac{1}{n} < x',x''< a+\frac{1}{n} \}$
2026-03-26 21:27:22.1774560442
Clarification of definition of lim sup of a set.
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I believe that the correct interpretation is
$$\limsup\limits_{n\to\infty}\big(\sup\{ |f(x')-f(x'')| : a-\frac{1}{n} < x',x''< a+\frac{1}{n} \}\big)$$