Can we update the data context of a WPF control in a non-UI thread?

Say we have a Label that has MyClass as data context, and bind Content to MyProperty:

<Label Name="label" Content="{Binding MyProperty}" />,

where MyClass is simply:

public class MyClass : INotifyPropertyChanged
{
    int _myField;
    public int MyProperty
    {
        get
        {
            return _myField;
        }
        set
        {
            _myField = value;
            PropertyChanged(this, new PropertyChangedEventArgs("MyProperty"));
        }
    }
    public event PropertyChangedEventHandler PropertyChanged;
}

In a non-UI thread, we can do myClass.MyProperty = "updated" to update the content of the label, but we cannot do label.Content = "updated" directly. Is that correct?

My own answer:

Here's what I've found:

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