The XMLStreamWriter and XMLEventWriter interfaces in Java's StAX (Streaming API for XML) API allow you to create and write XML documents in a streaming fashion. The XMLStreamWriter interface provides a lower-level API for writing XML documents, while the XMLEventWriter interface provides a higher-level, event-based API that allows you to create and write XML events as they occur.

Here's an example of using the XMLEventWriter interface to write events to an XML document:

import javax.xml.stream.*;
import javax.xml.stream.events.*;

import java.io.*;

public class StAXExample {

    public static void main(String[] args) throws Exception {
        XMLOutputFactory factory = XMLOutputFactory.newInstance();
        XMLEventWriter writer = factory.createXMLEventWriter(new FileWriter("example.xml"));
        XMLEventFactory eventFactory = XMLEventFactory.newInstance();
        StartDocument startDocument = eventFactory.createStartDocument();
        writer.add(startDocument);
        StartElement startElement = eventFactory.createStartElement("", "", "root");
        writer.add(startElement);
        Characters characters = eventFactory.createCharacters("Hello, world!");
        writer.add(characters);
        EndElement endElement = eventFactory.createEndElement("", "", "root");
        writer.add(endElement);
        EndDocument endDocument = eventFactory.createEndDocument();
        writer.add(endDocument);
        writer.flush();
        writer.close();
    }
}

In this example, we create an XMLOutputFactory object, which is used to create an XMLEventWriter object. We pass the name of the output XML file to the createXMLEventWriter() method to create a new writer for that file.

We then create XMLEvent objects using an XMLEventFactory object and add them to the writer using the add() method. In this case, we add a StartDocument event, a StartElement event for a root element, a Characters event containing the text "Hello, world!", an EndElement event for the root element, and an EndDocument event.

Finally, we flush the writer to ensure that all events have been written to the output file, and close the writer.

Note that the XMLEventWriter interface provides a higher-level, more convenient API for creating and writing XML documents than the lower-level XMLStreamWriter interface. However, it may be slightly slower and require more memory than the XMLStreamWriter interface, depending on the specific requirements of your application.