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The out-of-universe answer is the Dredd universe is a satire of an overpopulated, over-urbanized police state and not intended to make scientific sense.

That said, just how long could billions of people keep breathing if the Earth's oxygen cycle broke down? A long time. The Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O² and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO² then to too little O². I'll leave that for someone else to work out.

The out-of-universe answer is the Dredd universe is a satire of an overpopulated, over-urbanized police state and not intended to make scientific sense.

That said, just how long could billions of people keep breathing if the Earth's oxygen cycle broke down? A long time. The Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O₂ and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO₂ then to too little O₂. I'll leave that for someone else to work out.

Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O² and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO² then to too little O². I'll leave that for someone else to work out.

The out-of-universe answer is the Dredd universe is a satire of an overpopulated, over-urbanized police state and not intended to make scientific sense.

That said, just how long could billions of people keep breathing if the Earth's oxygen cycle broke down? A long time. The Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O² and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO² then to too little O². I'll leave that for someone else to work out.

Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O² and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO² then to too little O². I'll leave that for someone else to work out.

Earth's atmosphere is really, really, really, really big compared to puny humans (though not their machines).

A single human uses about 550 liters of pure oxygen per day. Not air, oxygen. At an atmospheric density of about 1.2 g/L that's about 660 g or 0.66 kg per person per day or 240 kg per person per year.

The atmosphere of the Earth weighs about 5.15e18 kg. 3/4 of that is within 11km of the surface, so let's use that: 3.86e18 kg. How much of that is oxygen? Oxygen is about 21% by volume with the rest being nitrogen and 1% miscellaneous that I'll ignore. But we want the percentage of oxygen by mass.

We can use the density of those gases to work out their mass ratios in air. 1.331 g/L for O² and 1.205 g/L for air at normal temperature and pressure.

1 liter of air weighs 1.205 g. 21% of the volume is oxygen, so it contributes 0.21 * 1.331 g/L = 0.28g. Divide them to get the mass-ratio of oxygen: 0.28g / 1.205g = 23%.

23% of 3.86e18 kg is 8.9e17 kg. That's a decent approximation of how much oxygen is in the atmosphere. Humans can survive as low as 17% oxygen, 6.6e17 kg, so they can safely consume 2.3e17 kg.

How long will it last?

2.3e17 kg / 240 kg per person per year = 9.6e14 person-years

Lacking a census for the Judge Dredd universe, I'll use 10 billion people or 1e10. They will have 9.6e4 or 96,000 years of breathing what's left in the atmosphere before there is a problem.

The bigger problem will be the build up of carbon dioxide in the atmosphere, we're far more sensitive to too much CO² then to too little O². I'll leave that for someone else to work out.