when browsing an e-commerce catalog, if a user selects a size on the size filter, is it safe to assume that the same size will be selected when the user wants to buy the product on the product page? therefore the size selected in the price filter can be auto selected on the product page
It sounds like a great idea with the exception that you can't guarantee who the user is buying for and therefor can't guarantee that the size you have selected is either theirs or is suitable for the person they are buying for.
If you do use this then I think you really have to make sure the user is aware that it's happening otherwise you may end up with lots of error purchases and that will harm the brand.
That would be a nice behaviour, to default the size in the product page to the filter selection. However you want to take care of instances whereby user buy without confirming their sizes. By not selecting the size in advance for them, you forced them to make the decision of choosing and hence reduce the chance of error or goods returned.
To handle such situation, you might want to highlight or emphasized the "size" select box to draw the user's attention to the size being selected. Don't forget to measure if this auto selection of size improves conversion.