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Products of quasi-continuous functions. (English) Zbl 0755.26002
The following theorem is proved: A cliquish function $$h:R\to R$$ is the product of $$n$$ quasi-continuous functions iff each of the sets $$\{x:h(x)=0\}$$, $$\{x:h(x)<0\}$$, $$\{x:h(x)>0\}$$ is the union of an open set and a nowhere dense set. Moreover, if $$h$$ is Lebesgue measurable (resp. of the Baire class $$\alpha)$$, then the factors can be taken to be Lebesgue measurable (resp. of the Baire class $$\alpha)$$.

##### MSC:
 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A30 Singular functions, Cantor functions, functions with other special properties
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##### References:
 [1] BLEDSOE W. W.: Neighbourly functions. Proc. Amer. Math. Soc. 3, 1952, 114-115. · Zbl 0046.40301 · doi:10.2307/2032465 [2] GRANDE Z.: Sur les functions cliquish. Časop. Pěst. Mat. 110, 1985, 225-236. · Zbl 0579.54009 · eudml:21592
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