Let (rj) be a Rademacher sequence of random variables – that is, a sequence of independent random variables, with
, for each j. A biorthogonal system
in a Banach space X is called an RUC-system[l] if for every x in [ej] (the closed linear span of the vectors ej), the series
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0305004100068055/resource/name/S0305004100068055_eqnU1.gif?pub-status=live)
converges for almost every ω. A basis which, together with its coefficient functionals, forms an RUC-system is called an RUC-basis. A biorthogonal system
is an RLTC-svstem if and only if there exists 1 ≤ K < ∞ such that
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0305004100068055/resource/name/S0305004100068055_eqn1.gif?pub-status=live)
for each x in [ej]: the RUC-constant of the system is the smallest constant K satisfying (1) (see [1], proposition 1.1).