Let Sigma(infinity)(i=1) c(i)R(i)(x) be the Rademacher series, where {R-i(x)}(i=1)(infinity) is the classical Rademacher function system and {c(i)}(i=1)(infinity) is an arbitrary real number sequence. In this paper, we first show that the value range of the Rademacher series at any subinterval of [0, 1] is R boolean OR {+/- 8} when {c(i)}(1)(infinity) is an element of l(2)\l(1). This result provides us with the basic facts that when {c(i)}(1)(infinity) is an element of l(2)\l(1), the Rademacher series cannot converge to an approximate continuous function, and there is no approximate limit at a...
