How to redirect unittest stream to the logging module

Stream2Logger.py

class Stream2Logger(object):

    def __init__(self, stream, logger, level):
        self._stream = stream
        self._logger = logger
        self._level = level
        self._buffer = []

    def write(self, message):
        self._buffer.append(message)
        if "\n" in message:
            self.flush()

    def flush(self):
        if self._buffer:
            message = "".join(self._buffer)
            if "\n" in message:
                self._logger.log(self._level, message.rstrip())
                self._buffer = []
            else:
                self._buffer = [message]
  

test.py

if __name__ == '__main__':
    suite  = unittest.TestSuite()
    # suite.addTest(...)
    logger = logging.getLogger('dummmy')
    stream = Stream2Logger(sys.stderr, logger, logging.ERROR)
    unittest.TextTestRunner(stream=stream, verbosity=2).run(suite)