Cross-Threading binding updates with WPF for RPH. I have no idea if this is best practice, but it seems to work.

MainWindow.cs

namespace MyApplication {
    public partial class MainWindow
    {
        private readonly ViewModel _vm;
        private bool _close;

        public MainWindow()
        {
            InitializeComponent();

            _vm = new ViewModel();
            DataContext = _vm;
            var thread = new Thread(SomeMethod);
            thread.Start();
        }

        /// <summary>
        /// Raises the <see cref="E:System.Windows.Window.Closing"/> event.
        /// </summary>
        /// <param name="e">A <see cref="T:System.ComponentModel.CancelEventArgs"/> that contains the event data.</param>
        protected override void OnClosing(CancelEventArgs e)
        {
            _close = true;
            base.OnClosing(e);
        }

        private void SomeMethod()
        {
            for (var i = 0;! _close; i++)
            {
                Thread.Sleep(TimeSpan.FromSeconds(2));
                _vm.SomeText = String.Format("{0} many times", i);
            }
        }
    }
}

MainWindow.xaml

<Window x:Class="MyApplication.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">
        <Label Content="{Binding SomeText}"/>
</Window>

ViewModel.cs

namespace MyApplication {
  public class ViewModel : INotifyPropertyChanged
    {
        private string _someText;
        public string SomeText
        {
            get { return _someText; }
            set
            {
                if (_someText != value)
                {
                    _someText = value;
                    OnPropertyChanged();
                }
            }
        }

        public event PropertyChangedEventHandler PropertyChanged;

        protected virtual void OnPropertyChanged([CallerMemberName] string propertyName = null)
        {
            var handler = PropertyChanged;
            if (handler != null) handler(this, new PropertyChangedEventArgs(propertyName));
        }
    }
}