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In order to get notified when a dependency property value changes, you can use the DependencyPropertyDescriptor.AddValueChanged function to register your own listener.

A simple example that displays the width of the window in a label:

public Window1()
{
InitializeComponent();

DependencyPropertyDescriptor widthDesc = DependencyPropertyDescriptor.FromProperty(Window.WidthProperty, typeof(Window));

if (widthDesc != null)
{
widthDesc.AddValueChanged(this, this.OnValueChanged);
}
}

private void OnValueChanged(object sender, EventArgs args)
{
txtLabel.Text = this.Width.ToString();
}