Not in a way meaningful to assessing infectious risk, no.
I consider outdoor air to be unshared, except in cases of large dense crowds (such as say outdoor festivals or sporting events).
I consider risky shared air to be indoor air with one or more other individuals that are not known to be taking infection-prevention precautions.
One can measure CO₂ as a proxy to rebreathed air fraction.
For example, a CO₂ reading of 2300ppm (common in a small or medium room with a few others, or larger rooms with a crowd or conference room, or in a car) means 5% of your air is rebreathed (5% of your intake is output from another person's lungs).
A way to think about this is we take ~20 breaths a minute on average. So in that scenario, it would be equivalent to one breath every minute coming directly from someone else's lungs. If they happen to be contagious with an airborne contagion (such as Covid, or influenza, or RSV), there's a high likelihood that you will catch it if you're spending more than a short time in that environment.
There are nuances, such as maybe the air is being scrubbed (eg by a HEPA filter) which won't affect the CO₂ levels but will drastically lower the infectious risk of that environment.
> One can measure CO₂ as a proxy to rebreathed air fraction.
On this topic, I got a CO₂ meter fairly recently and was shocked how quickly it spikes with a couple of people in a car with the windows up and on recirculate. Easily over 2000 after a few minutes. I have to remind myself regularly when it's really hot or cold outside to keep the vent setting on fresh air.
I had a Jaguar that had an air quality sensor that would switch to recirc based on particulates and then back to fresh air when the threshold indicated.
