An answer for Australia; applicable statues are very specific so most of what is allowed flows from common law.
There are a number of issues:
- Different rules apply to images and audio,
- These apply irrespective of the nature of the space (public or private),
- Warrants and other law-enforcement laws may make this permissible.
Photographs and Video
Starting with photographs and video, from How do laws affect photography of non-humans in public when people may be in the frame?
In R v Sotheren (2001) NSWSC 204 Justice Dowd said “A person, in our society, does not have a right not to be photographed.”
In general, you can take photos of people when you are on public property or private property (which includes inclosed public land e.g. public schools) where you have permission to be (and to photograph from). You can photograph into private property using any technology legally available.
There are limitations mainly related to voyeurism and commercial use, which are discussed at http://www.4020.net.
The recording of audio is more restricted, probably because audio recording has a longer history as a technology and therefore more cause and opportunity for legislative involvement.
In Australia, it is:
- legal to record a conversation with the permission of all of the participants,
- illegal to make a secret recording with anything connected to the telephone system - this includes Wi-Fi that then goes thru an ADSL line etc.,
- legal to make a secret recording of what comes out of the speakers of a telephone or computer connected to the internet by a party to the conversation,
- legal to make a secret recording of a face-to-face conversation by a party to the conversation,
- illegal to make a secret recording of any conversation that you are not a party to.
So, we can answer your supplementary questions without needing to determine if the gym is public (it isn't, by the way):
- Images are legal,
- Audio is not.
So why does the nature of the space make a difference? Well, whenever you enter private land, you do so with the common law understanding that you will abide by any reasonable and lawful requirements that the owner of that land requests of you.
So, if they ask you not to take photographs or not take video or audio recordings then you must not do so; if you ignore their requests then you are trespassing i.e. you no longer have permission to be on the property.
Now, you do not need permission or prohibition to be explicit. Implicit permission or prohibition is subject to the reasonable person test; for example, a shopping centre does not have to explicitly grant permission to photograph in the mall space nor does it have to specifically prohibit it in the toilets - both of these are things the reasonable person could infer.
This is a pretty good guide to public space.
In general, to be true public space, it must be:
- publicly owned (i.e. by a government - spaces owned by government owned corporations or public trusts are not public e.g. Sydney Trains railway stations are not public)
- open to the public (e.g. military bases are publically owned but not public spaces)
- currently open to the public (e.g. public parks are public during their opening hours and not-public when closed)
- currently not subject to restrictions (e.g. streets may be closed for parades or police operations rendering them non-public at those times)
Public spaces are government owned areas that are at the specific time open to the public (i.e. anyone) without restriction.
Neither an office nor a gym are public; they are both private (even if their owner is a government); you must abide by whatever rules their owners give.
If you have explicit or implicit permission:
- You can take images of people without their permission but you would need their permission to use the images commercially,
- You can make audio recordings with their permission or without their permission if you are a party to the conversation.