A Riesz spectrum for a measurable set 
of finite positive Lebesgue
measure is a frequency set 
for which the exponential
functions 
, 
, form a Riesz
basis of 
. This relaxes the orthonormal-basis condition
for an ordinary spectral set (Christensen 2016, Lee
2026).
Lee (2026) proved that no Riesz spectrum exists for
 |
whenever 
tends to zero. No additional relative-size condition is imposed on the intervals
or intervening gaps. For example, 
gives 
,
a set of Lebesgue measure 
. The assertion concerns this alternating class, rather
than every countable union of intervals.
