2

I am writing a paper and using such a notation. Do you think that it is mathematically a reasonable notation?

$$ \hat{{\cal{P}}}_{i}=\{\hat{Q}: \hat{Q}_i|G_i[q_1/q_0<t]\stackrel{i=1}{\underset{i=0}{\gtreqqless}}Q_i|G_i[q_1/q_0<t] \}, $$

Thank you very much.

EDIT: so I need to do in this way?

$$ \hat{{\cal{P}}}_{0}=\{\hat{Q}: \hat{Q}_0|G_0[q_1/q_0<t]\leq Q_0|G_0[q_1/q_0<t]\}, $$

and

$$ \hat{{\cal{P}}}_{1}=\{\hat{Q}: \hat{Q}_1|G_1[q_1/q_0<t]\geq Q_1|G_1[q_1/q_0<t]\}, $$

Seyhmus Güngören
  • 7,848

1 Answers1

2

Apart from the typesetting issues (e.g. the outer braces and hats are too small), the object in the middle is difficult to parse and takes up too much room. Some alternatives:

  1. If these are nonzero numbers, divide one by the other, name the result, and compactly say that the quotient is bigger (resp. less) than 1, if $i=0$ (resp. $i=1$). This has the advantage of emphasizing the close similarities between the two sides.

  2. If these are possibly zero numbers, subtract one from the other and continue as above.

  3. Since the only values you're considering are $i=0,1$, then eliminate $i$ altogether and simply define the two things you want.

Followup: Try $H_i=G_i[q_1/q_0<t]$, that will make your two expressions much shorter.

vadim123
  • 82,796
  • Is the problem mainly due to the greater and less equal term which is driven by $i=0,1$? I could write them in two equations but it would not seem compact. And the rest, namely $Q_i|G_i[q_1/q_0<t]$ is understood as the measure $Q_i$ given the measure $G_i$ for which we have $[q_1/q_0<t]$? – Seyhmus Güngören Jun 08 '13 at 00:26