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Breathing in Innsbruck?

Travel Info
A friend of mine is going to Innsbruck, Austria this summer, so he asked a question which I think is rational:
Since Innsbruck and the areas around it are mountain areas (Innsbruck itself is 500 metres above sealevel, surrounding areas are between 1000-2000 meters), does this mean that newcomers to this area (especially if they originally live in areas not that high) experience difficulty breathing? do these areas have thin air which makes respiration harder?

Travel Tips

I was in Innsbruck as a teenager and don't remember having any trouble breathing. I'm from an area just about even with sea level.