There are many mentions in JA's novels of a woman having X thousand pounds. The P&P FAQ (see link) discusses the legalities of how such settlements were made.

How were such settlements or fortunes advertised? How did people know that Miss Mary King had ten thousand pounds? I can't imagine that it would be proper for her to shout the information from the rooftops, or advertise it in the local paper.

If a young man is given to understand that a young lady has ten thousand pounds, how can he assure himself of the truth of this, prior to becoming engaged? Given that he cannot honourably break the engagement once made, it would seem to be very much to the advantage of a lady with three thousand pounds to have it generally believed that she had ten thousand.So long as she accepts an honourable suitor, the lie will not be refuted until after it has achieved its purpose. Unless her suitors are so gauche as to discuss such matters with her, she may even be able to disclaim knowledge of the inflated fortune attributed to her.

There are aspects of all this in Northanger Abbey, where the Moreland family's fortune is variously mis-estimated.

(For that matter, how is it that everyone is so knowlegable about the fortunes of the young men? E.g. it is common knowledge that Mr. Bingley has one hundred thousand pounds (hence interest of five thousand per annum) and Mr Darcy has ten thousand pounds per annum.)