The subindependence of coordinate slabs in l(p)(n) balls

It is proved that if the probability P is normalised Lebesgue measure on on e of the l(p)(n) balls in R-n, then for any sequence t(1),t(2),...,t(n) of positive numbers, the coordinate slabs {\x(i)\ less than or equal to t(i)} are subindependent, namely, [GRAPHICS] A consequence of this result is that the proportion of the volume of the l( 1)(n) ball which is inside the cube [-t, t](n) is less than or equal to f(n )(t) = (1 - (1 - t)(n))(n). It turns out that this estimate is remarkably a ccurate over most of the range of values of t. A reverse inequality, demons trating this, is the second major result of the article.