for a person
or for a collection of assets
Both of these are commonly measured, simplistically, in terms of money.
There are two types of people in the world - those who believe that wealth is fixed, and those who believe that it is created.
The Fixed Wealth Model
If the amount of wealth is largely fixed, then people who are wealthy have gained that wealth through taking it from others. The fact that someone has a mansion means that someone else cannot have a mansion. Further - the utility (wealth) curve has a reducing first derivative. This means that the utility gained from an extra dollar reduces as the person gets richer. Put more simply - taking $1000 a rich person doesn't reduce their lifestyle by much. On the other hand, giving that $1000 to a poor person may stop them from starving.
Further, proponents of this model normally see trade (even voluntary trade) as something which makes some people much richer than others, therefore trade ultimately makes one party richer, and the other poorer.
Proponents of this model believe that the greater good is achieved through distribution of wealth, and minimum of voluntary trade. If those who have a great deal of wealth can be coerced into giving it to those who have less, society ends up better off.
Generally, the fixed-wealth school are communists or socialists. They see the poverty in third world nations as a product of trading with the the first world, and see globalization as a tool of third world exploitation.
The Created Wealth Model
This is based on the notion that all wealth has been created by someone's work and effort. If someone builds a warehouse, a machine, or a house to live in it, this is something that did not exist before - it has been created by their mind and their effort. Nothing is stopping anyone else from building a similar machine or building.
Proponents of this model normally believe that someone who has gained wealth through voluntary trade with others has not only created the wealth they have, but added to the wealth of others by trading with them. If others traded voluntarily with them, they must have been better off due to the trade. Hence they have increased other's total wealth in becoming wealthy themselves.
If all wealth is created by human effort, then the distribution of wealth is not important - everyone can become rich (or at least well-off) through their own effort. In fact any involuntary distribution removes incentives to create wealth (the more wealth you create, the more you are forced to give away) and creates moral hazard - (people get rewarded for placing themselves in situations of need) and utility is decreased by the distribution.
Fixed or Created?
The fixed-wealth school generally have no understanding, or an extremely warped understanding of history. The wealth enjoyed by the first world at the start of the 21st century is beyond the wildest dreams of the population even a century ago. It did not just materialize from careful studies of more equitable welfare distribution formulas. This wealth is not just fixed - it has been created by people who have been free to pursue their own visions, to make their own mistakes, and to profit from the wealth their ideas created.
It apparently doesn't occur to the fixed-wealth school that the nations they want to protect from globalization have always been poor and corrupt. They simultaneously claim that trading with poor nations makes them poorer, and also that countries which the first world refuses to trade with (such as Cuba, Iraq and North Korea) are poor as a result of sanctions. Trading with others is bad, but not trading with them is even worse?
However while the fixed-wealth school is wrong, they are not totally wrong.
Every machine, or building uses some asset which is non-replenishable, the fact that a particular machine uses a quantity of metal means that no-one else can use that metal. They can mine and smelt other metal, but the total available metal has been reduced by their use of it. Likewise everyone who builds a house on some land prevents someone else from using that land. They may be able to build on some other land - but it is likely to be further from the centers of production, poorer land - less productive land.
So the truth lies somewhere between the two extremes, but where? A little thought about relative costs should clear it up. Compare the cost of a mining lease for a tonne of metal ore compared to the cost of the consumer items which that tonne will create. The cost of the (as yet un-mined) ore is the value of the fixed wealth - everything else is value added by someone's planning, skill, ingenuity and hard work. Clearly the vast bulk of the wealth is in the value-adding.
The cost of land though, provides a different extreme. What is the cost of a vacant block of inner city land, compared to the cost a similar piece of land with a house already on it? Most of the cost is in the land.
However we should be wary of a naive analysis here. Anyone can buy a quarter acre of land miles from anywhere for a few weeks wages. The value is in the infrastructure nearby. The fact that someone takes over a quarter acre block close to a small town, and that block eventually becomes an inner suburb of a major city does not make someone else worse off. There is still the opportunity to buy a cheap quarter acre block on the outskirts of that major city, and that will afford all the benefits which the quarter acre block in the town originally did (probably more, actually). The land is valuable because it offers the opportunity to trade with a large number of people - as does (now) the block on the outskirts. The reason that the inner city block became valuable was because many people chose to live nearby and trade with each other - the same pattern which occurs on the outskirts of the major city.
Someone who inherits the inner-city block has an advantage over the person who has to buy on the city outskirts - because they are closer to the center of production, and therefore can trade with more wealthy people, but inheritance is discussed elsewhere in this work.
In short, the fixed-wealth schools have a point, but they are 95% wrong, and they are creatures of envy. When they see someone else who has done well, they don't say 'good on them', they don't try to learn from them, they don't see wealthy people as good trading partners - they just want to loot their wealth. They claim to stand for fairness and compassion, when they are actually just in denial of their own greed, laziness and incompetence.