A Lebesgue measurable function A is a (q, N)-atom for [H.

If 1/q - 1/r < [mu] [less than or equal to] 1/q, then for any Lebesgue measurable function a satisfying

A is [Laplace] [cross product] B measurable if A belongs to the [sigma]--algebra generated by all sets of the form J x D, where J is

Lebesgue measurable in I and D is Borel measurable in R.

The function u: J [right [arrow] U, is the control function which is a

Lebesgue measurable where U = [0, a].

s](T,Z) the space of all (equivalence classes of) strongly

Lebesgue measurable functions w : T [right arrow] Z such that t [right arrow] [[parallel]w(t)[parallel].

alpha]] (t) is

Lebesgue measurable for any [alpha] [member of] [0,1].

The intersection with a Bernstein set has cardinality c also for sets in other rather wide perfect-saturated classes, such as

Lebesgue measurable sets with positive measure or non-meagre sets with the property of Baire.

A] of a

Lebesgue measurable set A is defined and several properties of [g.

n]) of Lebesgue measurable subsets of R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Accordingly we can have a sequence of Lebesgue measurable subsets of R such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In the general case of any

Lebesgue measurable function f with bounded variation M > 0 the inequality of Lemma 3.

M,[omega]] (T) the class of

Lebesgue measurable functions f : T [right arrow] C satisfying the condition