Check if a string is null or empty in XSLT

Absent of any other information, I'll assume the following XML:

<group>
    <item>
        <id>item 1</id>
        <CategoryName>blue</CategoryName>
    </item>
    <item>
        <id>item 2</id>
        <CategoryName></CategoryName>
    </item>
    <item>
        <id>item 3</id>
    </item>
    ...
</group>

A sample use case would look like:

<xsl:for-each select="/group/item">
    <xsl:if test="CategoryName">
        <!-- will be instantiated for item #1 and item #2 -->
    </xsl:if>
    <xsl:if test="not(CategoryName)">
        <!-- will be instantiated for item #3 -->
    </xsl:if>
    <xsl:if test="CategoryName != ''">
        <!-- will be instantiated for item #1 -->
    </xsl:if>
    <xsl:if test="CategoryName = ''">
        <!-- will be instantiated for item #2 -->
    </xsl:if>
</xsl:for-each>

From Empty Element:

To test if the value of a certain node is empty

It depends on what you mean by empty.

• Contains no child nodes: not(node())
• Contains no text content: not(string(.))
• Contains no text other than whitespace: not(normalize-space(.))
• Contains nothing except comments: not(node()[not(self::comment())])

test="categoryName != ''"

Edit: This covers the most likely interpretation, in my opinion, of "[not] null or empty" as inferred from the question, including it's pseudo-code and my own early experience with XSLT. I.e., "What is the equivalent of the following Java?":

// Equivalent Java, NOT XSLT
!(categoryName == null || categoryName.equals(""))

For more details e.g., distinctly identifying null vs. empty, see johnvey's answer below and/or the XSLT 'fiddle' I've adapted from that answer, which includes the option in Michael Kay's comment as well as the sixth possible interpretation.