# Blackboard bold variants for Greek letters

It is common (or it used to be) to use a blackboard-bold variant of \mu to denote roots of unity in some mathematical papers. However, despite searching (several times, periodically over several years) I have never been able to locate any package or technique that makes this possible, other than using Metafont or possibly hunting through the font definitions to see if it is something I can create a variant of (along the lines of the suggestions in Section 8 of the Comprehensive LaTeX symbol list).

Thus far, I haven't been sufficiently motivated to learn how to do any of this (although it probably would have resulted in a net time savings), and I feel like I cannot be the only person who would have tried. Is anyone aware of an existing way to produce this character?

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Unicode contains only four double-struck Greek letters: ℽℼℾℿ (γπΓΠ), and since the Unicode repertoire is quite comprehensive (and much larger than the Comprehensive Symbols List), I'd conjecture that this character is very uncommon. Could you give an example where this character is used? – Philipp Sep 25 '10 at 14:54
So far as I know, the only users of this symbol are probably certain specific typies of mathematician, so I would agree that it is very uncommon. It appears on this page in J. S. Milne's "Etale cohomology": books.google.com/… – Tyler Lawson Sep 25 '10 at 22:51
Barbara Beeton at the Ams is still collecting math symbols that are not in Unicode yet, so could you send her this question as well along with the example? (bnb at ams dot org) – Taco Hoekwater Sep 26 '10 at 7:25
@Taco: I agree. AFAIK the Unicode consortium holds the position that every character that is in use should be encoded. If someone can prove that mathematicians do use the character in question, there is a high chance that it will be added to the Unicode repertoire. – Philipp Sep 26 '10 at 11:09
@coarsemodule: Thanks for the example. The character in question looks more like a superposition of two µ's than a double-struck µ—compare the ℤ directly in front. – Philipp Sep 26 '10 at 11:13

The mbboard package provides blackboard bold Greek letters, and the letter you want is \bbmu. However, I don't know if you like how the symbol looks. (I don't like it, actually.)

The mathbbol package with the bbgreekl option also provides (a possibly nicer version of) \bbmu: Use \usepackage[bbgreekl]{mathbbol} in the preamble. The disadvantage is that the package also redefines \mathbb; see this post for possiblities to avoid this.

Note that lowercase epsilon is typeset with \bbespilon (sic).

Edit: I just realised that the mbboard package redefines \mathbb, too. If you don't like this, then an easy solution is to load the amssymb package after the mbboard package. This gives you the "usual" blackboard bold letters, and you can still use \bbmu and friends.

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Thanks for this. I looked at both options, and they do provide the functionality advertised. (I actually prefer the version provided by the mbboard package, as the mathbbol version is quite blocky along its edge.) Perhaps a version closer to the standard tex \mu symbol would be ideal, but these are certainly workable. – Tyler Lawson Sep 26 '10 at 14:46

Another font set that can provide this is MathTime Professional II fonts (mtpro2) from PCTeX. The web site mentions some journals that use these fonts.

The fonts are non-free and, to achieve what is wanted here are, chargeable (the non-free but no-cost 'lite' version does not include the 'blackboard bold italic' and 'holey bold italic' fonts which the two samples below use, using a simple redefinition of \mathbb). The outputs are just .pngs of screenprints so don't use these to judge the resolution of the original fonts.

\documentclass[12pt]{article}
\usepackage[mtpbbi]{mtpro2}
\begin{document}
$\mathbb{\mu} , \mathbb{M}$     % assuming '\Mu' = 'M'
\end{document}


\documentclass[12pt]{article}
\usepackage[mtpbbi]{mtpro2}
\begin{document}
$\mathbb{\mu} , \mathbb{M}$
\end{document}


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I also spent a lot of time on the issue and found nothing satisfactory. So I made up my own blackboard bold mu and alpha:

\documentclass{minimal}
\usepackage{amssymb}
\newcommand{\Balpha}{\mbox{$\hspace{0.12em}\shortmid\hspace{-0.62em}\alpha$}}
\usepackage{xcolor}
\usepackage{graphicx}
\newcommand{\Bmu}{\mbox{$\raisebox{-0.59ex} {$l$}\hspace{-0.18em}\mu\hspace{-0.88em}\raisebox{-0.98ex}{\scalebox{2} {$\color{white}.$}}\hspace{-0.416em}\raisebox{+0.88ex} {$\color{white}.$}\hspace{0.46em}$}{}}
\begin{document}
$\Balpha\quad\Bmu$
\end{document}


This produces

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+1 from new, in particular for the \Bmu. You could improve the \Balpha by using a \rule instead of the \shortmid. – Hendrik Vogt May 24 '13 at 6:58

Just for kicks, you could kludge together your own version which is similar to the symbol in the book you linked in the comments

\documentclass{minimal}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{graphicx}
\newcommand{\dmu}{$\mu$\hspace{-3.2pt}$\mu$\hspace{-5.7pt}\raisebox{-3.06pt}{\scalebox{1.6}{$\color{white}\cdot$}}}
\begin{document}
\dmu
\end{document}


Which produces,

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