How do you detect if a collection of values are distinct (unique) without storing them in memory

I have a class that stores values and detects if that set of values are distinct.

public class TextRecords
{
    public TextRecords()
    {
        Count = 0;
        TextInstanceDictionary = new Dictionary<string, int>();
    }

    public int Count
    {
        get;
        set;
    }

    public Dictionary<string, int> TextInstanceDictionary
    {
        get;
        set;
    }

    public void AddOrUpdateTextInstanceDictionary(string theText)
    {
        if (!TextInstanceDictionary.ContainsKey(theText))
        {
            TextInstanceDictionary.Add(theText, 1);
        }
        else
        {
            TextInstanceDictionary[theText] += 1;
        }
    }

    public bool AllValuesAreDistinct
    {
        get
        {
            return !TextInstanceDictionary.Any(kv => kv.Value > 1);
        }
    }
}

This works fine for small sets of values but is not scale in terms of memory usage and performance.

Is there a way to detect if a set of values are unique without storing them all in memory as I am doing in the approach above?

I am looking for reasonable small memory footprint while retaining a good level of speed.

I am aware of Bloom filters and read this answer. Is there any other methods to solve this very specific problem?

(Note: I have also reviewed this answer but this is a different problem. I am streaming in the values one by one so just need to know if I have or haven't seen that value before. The other answer is where you are presented with a fully populated collection and asked if the values are distinct).