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Where to put acronym/abbreviation explanation?

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I'm writing my thesis, and I use some acronyms in it.

For example "MDBs" = "Multilateral Development Banks".

Usually, I write "Multilateral Development Banks (MDBs)" the first time I cite it and then use "MDBs".

Now I have the case where the first time I use this acronym is in a table. In the ordinary text following the table I wrote "Multilateral Development Banks (MDBs)", but should I put a footnote also in the table?

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I assume you're using latex with autogenerated glossary, if not you probably should.

\usepackage[acronym]{glossaries}

\makeglossaries

\newacronym{MDBs}{MDBs}{Multilateral Development Banks}

If this is some acronym you will use more later, it's better to introduce it in the main text before it shows up in a table:

In this part of research we used \gls{MDBs}, the best stuff since slice bread, see \autoref{tab:table1}. 

\begin{table}[h]
    some stuff about \gls{MDBs}
\label{tab:table1}
\end{table}

If it is only used in this table and nowhere else there is little reason to make an acronym at all. Just spell it all out:

\begin{table}[h]
    some stuff about Multilateral Development Banks.
\label{tab:table1}
\end{table}

If you really need or want to introduce the acronym in the table, it makes more sense to expand it in the caption. I don't remember how to do it in tex macro:

\begin{table}[h]
    some stuff about Multilateral Development Banks^{1}.
\caption[Table about stuff]{This table contains stuff.  Acronyms: \gls{MDBs}, \gls{ABC}, ...}
\label{tab:table1}
\end{table}
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+0
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In the ordinary text following the table I wrote "Multilateral Development Banks (MDBs)", but should I put a footnote also in the table?

You could but I don't think it is necessary and I would not; I don't expect a reader to look at the table until they read the discussion about it. I would put the expansion somewhere in that discussion (and it sounds like you already have). A table does not have to stand alone; there isn't room to explain every label in the table. Readers understand that, and will refer to the discussion text to understand. One thing you might do is force the table to appear after the discussion text, in normal reading order, so nobody should encounter "MDB" before having read what it means.

(I am a PhD, author of several journal papers, I wrote two different Master's theses and my dissertation, and I peer review scientific journal papers; I have reviewed six thus far this year.)

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