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and that 
,
.Prove that both
and 
are convergent sequences and that 
.
,
that 
is a differentiablefunction and that
.
Show that there exists an
such
that 
.
is a continuous function and that
.Prove that
for
each 
.
Compute
and 
.
is a measure space and that 
.
Let 
be given.
such that 
whenever
and
.
such that 
and 
.
denote the Lebesgue measure on 
and let 
be any proper linear subspace of .
Prove that 
.
.
,
.
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