Making sure OnPropertyChanged() is called on UI thread in MVVM WPF app

In a WPF app that I'm writing using the MVVM pattern, I have a background process that doing it's thing, but need to get status updates from it out to the UI.

I'm using the MVVM pattern, so my ViewModel knows virtually nothing of the view (UI) that is presenting the model to the user.

Say I have the following method in my ViewModel:

public void backgroundWorker_ReportProgress(object sender, ReportProgressArgs e)
{
    this.Messages.Add(e.Message);
    OnPropertyChanged("Messages");
}

In my view, I have a ListBox bound to the Messages property (a List<string>) of the ViewModel. OnPropertyChanged fulfills the role of the INotifyPropertyChanged interface by calling a PropertyChangedEventHandler.

I need to ensure that OnPropertyChanged is called on the UI thread - how do I do this? I've tried the following:

public Dispatcher Dispatcher { get; set; }
public MyViewModel()
{ 
    this.Dispatcher = Dispatcher.CurrentDispatcher;
}

Then adding the following to the OnPropertyChanged method:

if (this.Dispatcher != Dispatcher.CurrentDispatcher)
{
    this.Dispatcher.Invoke(DispatcherPriority.Normal, new ThreadStart(delegate
    {
        OnPropertyChanged(propertyName);
    }));
    return;
}

but this did not work. Any ideas?