Market is just some place where supply and demand meets. From Mankiw Principles of Microeconomics 5ed pp 66:
A market is a group of buyers and sellers of a particular good or service. The buy- ers as a group determine the demand for the product, and the sellers as a group determine the supply of the product.
Markets take many forms. Sometimes markets are highly organized, such as the markets for many agricultural commodities. In these markets, buyers and sell- ers meet at a specific time and place, where an auctioneer helps set prices and arrange sales.
More often, markets are less organized. For example, consider the market for ice cream in a particular town. Buyers of ice cream do not meet together at any one time. The sellers of ice cream are in different locations and offer somewhat differ- ent products. There is no auctioneer calling out the price of ice cream. Each seller posts a price for an ice-cream cone, and each buyer decides how much ice cream to buy at each store.
Moreover, Mankiw talks about groups of buyers and sellers, but in many papers and research work it is any place where supply and demand meets even if the group size of each of the two groups would $n=1$.
However, you since tagged your question with GDP you should keep in mind the caveat that GDP is calculated as a final value of goods and services sold at formal markets. GDP completely ignore goods and services sold at black markets, or gray markets, or home production because there is obviously no way how statistical agencies can actually directly collect data on such activities (they could estimate them but that would make the whole measure less reliable so typically with GDP we settle for calculating it only for formal sectors - this however does not mean that black or gray markets or home production do not add value to the economy, they clearly do, it’s just it’s difficult to measure it).
many items high sold price considered rediculous by majority and merely accepted by a few people?
This does not matter. Under our (in economic science that is) most current understanding of value is that value is subjective. That is value is in the eye of beholder. There is no objective value for painting.
If someone is billing to pay \$10000000 for some abstract art then that means that the person values that art at the minimum at \$10000000. There is nothing ridiculous about that per se, that is simply the person's revealed preference.
For you to say that paying that much for a painting is ridiculous you have to either make a moral judgement or impose your preferences on other person.
A) economics does not deal with moral judgements, economics is science. A philosophers can squabble about whether buying the painting is ridiculous or not, we just care about what people themselves believe that has value.
B) every person will value all goods differently, there is no reason for picking valuation of 1 single person, and say that is valuation of everyone. If you care about measuring all value produced in the economy you want to record all goods and services at value at which all individuals valued them.
Now that is not possible because you can’t see into peoples heads, but market price represents the minimum value that good has to bring the individual (e.g. if you purchase ticket for a play for 10€ at minimum you are getting 10€ value), so GDP is recorded at market prices as our best of what is the economic value the good or service brings to individuals.
what is the boundary between non gdp counted and gdp counted services?
The boundary is whether the service is final (eg business to business services do not count) and whether the service was formally sold at some market (eg services at home between partners like cooing etc are not counted) but service for which you actually get some sort of invoice or bill are.
