How to call an async method from a getter or setter?

You can use Task like this :

public int SelectedTab
        {
            get => selected_tab;
            set
            {
                selected_tab = value;

                new Task(async () =>
                {
                    await newTab.ScaleTo(0.8);
                }).Start();
            }
        }

When I ran into this problem, trying to run an async method synchronicity from either a setter or a constructor got me into a deadlock on the UI thread, and using an event handler required too many changes in the general design.
The solution was, as often is, to just write explicitly what I wanted to happen implicitly, which was to have another thread handle the operation and to get the main thread to wait for it to finish:

string someValue=null;
var t = new Thread(() =>someValue = SomeAsyncMethod().Result);
t.Start();
t.Join();

You could argue that I abuse the framework, but it works.

You can create an event and invoke an event when the property is changed. Something like this:

private event EventHandler<string> AddressChanged;
public YourClassConstructor(){
     AddressChanged += GoogleAddressesViewModel_AddressChanged;
}
private async void GoogleAddressesViewModel_AddressChanged(object sender, string e){
      ... make your async call
}
private string _addressToSearch;
public string AddressToSearch
{
    get { return _addressToSearch; }
    set
    {
        _addressToSearch = value;
        AddressChanged.Invoke(this, AddressToSearch);
    }
}

Necromancing.
In .NET Core/NetStandard2, you can use Nito.AsyncEx.AsyncContext.Run instead of System.Windows.Threading.Dispatcher.InvokeAsync:

class AsyncPropertyTest
{

    private static async System.Threading.Tasks.Task<int> GetInt(string text)
    {
        await System.Threading.Tasks.Task.Delay(2000);
        System.Threading.Thread.Sleep(2000);
        return int.Parse(text);
    }


    public static int MyProperty
    {
        get
        {
            int x = 0;

            // https://stackoverflow.com/questions/6602244/how-to-call-an-async-method-from-a-getter-or-setter
            // https://stackoverflow.com/questions/41748335/net-dispatcher-for-net-core
            // https://github.com/StephenCleary/AsyncEx
            Nito.AsyncEx.AsyncContext.Run(async delegate ()
            {
                x = await GetInt("123");
            });

            return x;
        }
    }


    public static void Test()
    {
        System.Console.WriteLine(System.DateTime.Now.ToString("dd.MM.yyyy HH:mm:ss.fff"));
        System.Console.WriteLine(MyProperty);
        System.Console.WriteLine(System.DateTime.Now.ToString("dd.MM.yyyy HH:mm:ss.fff"));
    }


}

If you simply chose System.Threading.Tasks.Task.Run or System.Threading.Tasks.Task<int>.Run, then it wouldn't work.

You can simply do it like this:

public IEnumerable MyList
{
    get
    {
        Task.Run(async () => await MyAsyncMethod);
    }
}

But depending on the full context you could try to find another way of triggering your async method, for ex: when you call for MyList you could call first MyAsyncMethod..

I think my example below may follow @Stephen-Cleary 's approach but I wanted to give a coded example. This is for use in a data binding context for example Xamarin.

The constructor of the class - or indeed the setter of another property on which it is dependent - may call an async void that will populate the property on completion of the task without the need for an await or block. When it finally gets a value it will update your UI via the NotifyPropertyChanged mechanism.

I'm not certain about any side effects of calling a aysnc void from a constructor. Perhaps a commenter will elaborate on error handling etc.

class MainPageViewModel : INotifyPropertyChanged
{
    IEnumerable myList;

    public event PropertyChangedEventHandler PropertyChanged;

    public MainPageViewModel()
    {

        MyAsyncMethod()

    }

    public IEnumerable MyList
    {
        set
        {
            if (myList != value)
            {
                myList = value;

                if (PropertyChanged != null)
                {
                    PropertyChanged(this, new PropertyChangedEventArgs("MyList"));
                }
            }
        }
        get
        {
            return myList;
        }
    }

    async void MyAsyncMethod()
    {
        MyList = await DoSomethingAsync();
    }


}

I review all answer but all have a performance issue.

for example in :

string _Title;
public string Title
{
    get
    {
        if (_Title == null)
        {   
            Deployment.Current.Dispatcher.InvokeAsync(async () => { Title = await getTitle(); });
        }
        return _Title;
    }
    set
    {
        if (value != _Title)
        {
            _Title = value;
            RaisePropertyChanged("Title");
        }
    }
}

Deployment.Current.Dispatcher.InvokeAsync(async () => { Title = await getTitle(); });

use dispatcher which is not a good answer.

but there is a simple solution, just do it:

string _Title;
    public string Title
    {
        get
        {
            if (_Title == null)
            {   
                Task.Run(()=> 
                {
                    _Title = getTitle();
                    RaisePropertyChanged("Title");
                });        
                return;
            }
            return _Title;
        }
        set
        {
            if (value != _Title)
            {
                _Title = value;
                RaisePropertyChanged("Title");
            }
        }
    }

You can change the proerty to Task<IEnumerable>

and do something like:

get
{
    Task<IEnumerable>.Run(async()=>{
       return await getMyList();
    });
}

and use it like await MyList;