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# Continuous functions whose level sets are orthogonal to all polynomials
of a given degree

**Herold Dehling
**

Murad S. Taqqu

### Abstract:

*Let be any continuous non-negative
weight function on *** R** with .
We prove the existence of continuous
functions for
which the indicator functions of the level sets with their mean subtracted are orthogonal to all polynomials of
degree less than or equal to **k**. The result is used to settle an open problem
on empirical processes of long-range dependent sequences.