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I'd like to ask how to write notes under the table (in float) in LYX?

I found the following, but it is strangely written (how can a table be at the same time out and in the float???):

'Table inside float

This is more tricky, since the float is floating, and the footnotes are floating as well (which makes it very difficult to handle footnotes).

The easiest way is to put the table in a minipage (Insert→Box). This will always give you footnotes, but they are not part of the ordinary footnote apparatus, but placed directly underneath the table (and separately numbered). Note that the Box (Minipage) doesn't tolerate floats, so that the table itself should be outside a float (and, in this case, within the Box). This method can cause the table with footnotes to appear below any normal footnotes on the same page. A solution is to add \usepackage[bottom]{footmisc} to the preamble

(source: http://skalkoto.blogspot.com/2008/01/latex-and-footnotes.html (approve sites)). '

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If you want footnotes at the bottom of your table, numbered independently from the ‘general’ footnotes (with lowercase letters, for instance) you can do that with the threeparttable package.This requires editing your code. The general structure is the following:

\begin{table}
\begin{threeparttable}
\caption{...}
\begin{tabular}...% or {tabular*}
...42\tnote{a}&.... ...
\end{tabular}
\begin{tablenotes}
\item [a] the first note ...
\end{tablenotes}
\end{threeparttable}
\end{table}

If you want footnotes inserted at the bottom of the page, you have the more recent tablefootnotes package.

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    The OP asked about Lyx. The code provided by Bernard can be posted in its entirety in Latex mode in Lyx. It can also be inserted in Latex mode withint Lyx's table and table float elements. It took me a while to figure out that threeparttable requires an \item element in its tablenotes part. – Paul Rougieux Feb 16 '16 at 8:48
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You can insert footnotes in tables using a minibox based on the instruction on the Lyx wiki.

But as Bernard mentioned in his answer, notes inserted with the threeparttable package look nicer. I posted a Lyx file with 3 examples using the threeparttable package with Lyx's tables and table floats : threeparttable.lyx.

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