https://wiki.lojban.io/index.php?action=history&feed=atom&title=ma%27au ma'au - Revision history 2026-05-03T06:27:04Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=ma%27au&diff=9893&oldid=prev Nalvaizmiku: Import words via API 2026-01-13T15:36:14Z <p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> ma&#039;au<br /> ==== type ====<br /> experimental cmavo<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Mon Apr 2 17:12:13 2018<br />  <br /> == English ==<br /> === Definition #70586 - Preferred ===<br />  <br /> ==== selma&#039;o ====<br /> VUhU<br /> ==== definition ====<br /> <br /> Binary mekso operator: uniform probability MATH<br /> $A(X_2)u(X_1,X_2)$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;A&lt;/i&gt;(&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;)&lt;i&gt;u&lt;/i&gt;(&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;, &lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;)&lt;/span&gt; for input &lt;span class=&quot;MATH&quot;&gt;(&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;, &lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;)&lt;/span&gt; where &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is a number and &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; is a set or space. (See notes for details).<br /> <br /> ==== notes ====<br /> <br /> Establish (elsewhere) a universal set/topological space &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;&lt;/span&gt; and equip it with a measure &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;L&lt;/i&gt;&lt;/span&gt;; then &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; must be an� element of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;&lt;/span&gt;, and &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; must be a subset/subspace of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;&lt;/span&gt; and will be equipped with/inherit the same measure &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;L&lt;/i&gt;&lt;/span&gt; (restricted to it) and the appropriate topology. Let &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt; be the maximal non-discrete subset/subspace of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; (in other words, all non-discrete subsets/subspaces of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; are subsets/subspaces of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt;). The term &#039;&lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;A&lt;/i&gt;&lt;/span&gt;&#039; in the definition is a nonnegative-valued &#039;function&#039; which is defined on the category of sets; it produces the proper normalization (by being the reciprocal of the integral of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;u&lt;/i&gt;&lt;/span&gt; over &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;&lt;/span&gt; with respect to &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;L&lt;/i&gt;&lt;/span&gt; iff such is well-defined and finite and positive; otherwise, it is identically &lt;span class=&quot;MATH&quot;&gt;0&lt;/span&gt;). The term &#039;&lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;u&lt;/i&gt;&lt;/span&gt;&#039; in the definition is defined to be the sum of the indicator function (Kronecker delta) for &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt; (outputting &lt;span class=&quot;MATH&quot;&gt;1&lt;/span&gt; iff &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is an element &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt;, and outputting &lt;span class=&quot;MATH&quot;&gt;0&lt;/span&gt; otherwise) and the Dirac delta of: &lt;span class=&quot;MATH&quot;&gt;1&lt;/span&gt; minus the indicator function for the relative complement of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt; in &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; (id est: &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;<br /> &lt;br/&gt;&lt;i&gt;Y&lt;/i&gt;&lt;/span&gt;); it should be noted that all functions mentioned are defined on all of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;&lt;/span&gt; but have nonzero values according to only the previous description (in particular, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;u&lt;/i&gt; = 0&lt;/span&gt; identically in &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;O&lt;/i&gt;<br /> &lt;br/&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;); the indicator functions directly are functions of the input &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;X&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt;. See also: &quot;[[zdeltakronekre|zdeltakronekre]]&quot;, &quot;[[zdeltadirake|zdeltadirake]]&quot;.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/uniform distribution|uniform distribution]]&lt;/li&gt;&lt;li&gt;[[natlang/en/uniform probability distribution|uniform probability distribution]]&lt;/li&gt;&lt;li&gt;[[natlang/en/UPD|UPD ; uniform probability distribution]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Mon Apr 2 17:14:15 2018<br /> <br /> <br /> <br /> &lt;br&gt;&lt;font size=&quot;+1&quot;&gt;Examples&lt;/font&gt;<br /> &lt;hr/&gt;<br /> &lt;dl&gt;<br /> &lt;/dl&gt;<br /> &lt;/br&gt;<br /> === Etymology ===</div> Nalvaizmiku