Learn Hardcore Finnish: Tämä on yksityinen alue, pysy portin ulkopuolella. - This is a private area, stay outside the gate.

Because with the verb olla (“to be”) both the subject and the predicate nominative stay in the nominative case. Here alue is part of a classification (“This is a private area”), so it remains nominative.

What part of speech is yksityinen, and why doesn’t it take a separate case ending?

Yksityinen is an adjective modifying alue. Adjectives agree in case, number and gender with the noun they describe. Since alue is nominative singular, yksityinen is also nominative singular and doesn’t carry an extra ending.

Why is there a comma between the two clauses instead of a conjunction like ja?

In Finnish it’s perfectly normal to link two independent clauses with just a comma if you want brevity. On signs and warnings, omitting ja and using a comma makes the message more concise.

What mood and form is pysy, and who is it addressing?

Pysy is the singular second-person imperative of pysyä (“to stay”). It directly addresses one person, but on public notices it’s often used generically. If you wanted to address multiple people politely, you’d say pysykää.

Why is portin in the genitive case?

Because portin shows possession or relation (“of the gate”). When you combine it with a locative expression like ulkopuolella, the thing you stay outside of goes into the genitive.

What exactly is ulkopuolella, and what case is it?

Ulkopuolella comes from ulkopuoli (“outside part”) plus the adessive suffix -lla (location meaning “on”). So ulkopuolella means “on the outside”. Paired with genitive portin, it gives “on the outside of the gate” → “outside the gate.”

Could we say pysy portin ulkona instead of pysy portin ulkopuolella?

Not really. Ulkona means “outside” in a broad sense (“outside the house”), without specifying what you stay outside of. Portin ulkopuolella pinpoints the exact position: “on the outer side of the gate.”

Why start with Tämä on… rather than Yksityinen alue on tämä?

Finnish word order is flexible, but Tämä on… (“This is…”) foregrounds the object you’re talking about. In a sign you first draw attention to “this” thing and then describe its status (“private area”).

What’s the difference between pysy portin ulkopuolella and älä mene portin ulkopuolelle?

Pysy portin ulkopuolella (“stay outside the gate”) orders you to remain outside at all times.
Älä mene portin ulkopuolelle (“don’t go outside the gate”) forbids entering beyond the gate but doesn’t emphasize staying put.

Is it common to combine a declarative and an imperative with a comma on Finnish signs?

Yes. A short statement (Tämä on yksityinen alue) followed by an instruction (pysy portin ulkopuolella) connected by a comma is a very typical format for public notices.