<s>
In	O
mathematics	O
,	O
the	O
notions	O
of	O
prevalence	O
and	O
shyness	O
are	O
notions	O
of	O
"	O
almost	O
everywhere	O
"	O
and	O
"	O
measure	O
zero	O
"	O
that	O
are	O
well-suited	O
to	O
the	O
study	O
of	O
infinite-dimensional	O
spaces	O
and	O
make	O
use	O
of	O
the	O
translation-invariant	O
Lebesgue	O
measure	O
on	O
finite-dimensional	O
real	O
spaces	O
.	O
</s>
<s>
A	O
subset	O
of	O
is	O
said	O
to	O
be	O
locally	O
shy	O
if	O
every	O
point	O
has	O
a	O
neighbourhood	O
whose	O
intersection	O
with	O
is	O
a	O
shy	B-Algorithm
set	I-Algorithm
.	O
</s>
<s>
Any	O
finite	O
or	O
countable	O
union	O
of	O
shy	B-Algorithm
sets	I-Algorithm
is	O
also	O
shy	O
.	O
</s>
<s>
Any	O
shy	B-Algorithm
set	I-Algorithm
is	O
also	O
locally	O
shy	O
.	O
</s>
<s>
If	O
is	O
infinite-dimensional	O
,	O
then	O
every	O
compact	O
subset	O
of	O
is	O
shy	O
.	O
</s>
